* using log directory ‘/Users/ripley/R/packages/tests-devel/PsychoMatic.Rcheck’ * using R Under development (unstable) (2026-10-20 r90722) * using platform: aarch64-apple-darwin27.0.0 * R was compiled by Apple clang version 21.0.0 (clang-2100.3.34.1) GNU Fortran (GCC) 14.2.0 * running under: macOS Golden Gate 27.0.1 * using session charset: UTF-8 * current time: 2026-10-23 17:11:09 UTC * using option ‘--no-stop-on-test-error’ * checking for file ‘PsychoMatic/DESCRIPTION’ ... OK * checking extension type ... Package * this is package ‘PsychoMatic’ version ‘1.0.0’ * package encoding: UTF-8 * checking package namespace information ... OK * checking package dependencies ... OK * checking if this is a source package ... OK * checking if there is a namespace ... OK * checking for executable files ... OK * checking for hidden files and directories ... OK * checking for portable file names ... OK * checking for sufficient/correct file permissions ... OK * checking whether package ‘PsychoMatic’ can be installed ... OK * checking installed package size ... OK * checking package directory ... OK * checking ‘build’ directory ... OK * checking DESCRIPTION meta-information ... OK * checking top-level files ... OK * checking for left-over files ... OK * checking index information ... OK * checking package subdirectories ... OK * checking code files for non-ASCII characters ... OK * checking R files for syntax errors ... OK * checking whether the package can be loaded ... OK * checking whether the package can be loaded with stated dependencies ... OK * checking whether the package can be unloaded cleanly ... OK * checking whether the namespace can be loaded with stated dependencies ... OK * checking whether the namespace can be unloaded cleanly ... OK * checking loading without being on the library search path ... OK * checking use of S3 registration ... OK * checking dependencies in R code ... OK * checking S3 generic/method consistency ... OK * checking replacement functions ... OK * checking foreign function calls ... OK * checking R code for possible problems ... [14s/14s] OK * checking Rd files ... OK * checking Rd metadata ... OK * checking Rd cross-references ... OK * checking for missing documentation entries ... OK * checking for code/documentation mismatches ... OK * checking Rd \usage sections ... OK * checking Rd contents ... OK * checking for unstated dependencies in examples ... OK * checking installed files from ‘inst/doc’ ... OK * checking files in ‘vignettes’ ... OK * checking examples ... OK * checking for unstated dependencies in ‘tests’ ... OK * checking tests ... Running ‘testthat.R’ [157s/158s] [157s/158s] ERROR Running the tests in ‘tests/testthat.R’ failed. Complete output: > library(testthat) > library(PsychoMatic) > > test_check("PsychoMatic") ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) item1 0.715 0.000 0.000 item2 0.796 0.000 0.000 item3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) item1 0.011 0.000 0.000 item2 -0.017 0.000 0.000 item3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD G1 0.000 1.000 G2 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.952 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.795 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.018 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.108 0.987 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.986 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS `data`, `group`, and `sampling_weights` were ignored because `lambda` and `nu` were provided. the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 Loading required namespace: MASS ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.414 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i1 0.901 0.000 0.000 i2 0.763 0.000 0.000 i3 0.770 0.000 0.000 i4 0.671 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i1 0.059 0.000 0.000 i2 0.031 0.000 0.000 i3 0.043 0.000 0.000 i4 0.034 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD A 0.000 1.000 B -0.043 0.915 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason configural_parameter_matrices_invalid configural_parameter_matrices_invalid CONCLUSION Alignment invariance could not be evaluated (configural_parameter_matrices_invalid). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS Configural output must identify the same groups as `group`. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.710 0.000 0.000 i1 0.790 0.000 0.000 i3 0.745 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.008 A 0.108 0.992 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_vcov_invalid alignment_vcov_invalid CONCLUSION Alignment invariance could not be evaluated (alignment_vcov_invalid). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS `vcov` must be a finite numeric 12 x 12 matrix for these parameters. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_vcov_invalid alignment_vcov_invalid CONCLUSION Alignment invariance could not be evaluated (alignment_vcov_invalid). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS `vcov` must be symmetric within numerical tolerance. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_vcov_invalid alignment_vcov_invalid CONCLUSION Alignment invariance could not be evaluated (alignment_vcov_invalid). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS `vcov` must be positive semidefinite. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_vcov_invalid alignment_vcov_invalid CONCLUSION Alignment invariance could not be evaluated (alignment_vcov_invalid). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS Named `vcov` rows and columns must be identical, unique, and follow the sirt parameter order for `lambda` and `nu`. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason group_parameters_nonfinite_or_empty group_parameters_nonfinite_or_empty GROUP PARAMETERS Group Latent mean Latent SD B - - A - - CONCLUSION Alignment invariance could not be evaluated (group_parameters_nonfinite_or_empty). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason aligned_item_parameters_nonfinite_or_empty aligned_item_parameters_nonfinite_or_empty GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (aligned_item_parameters_nonfinite_or_empty). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason aligned_lambda_dimension_mismatch aligned_lambda_dimension_mismatch GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (aligned_lambda_dimension_mismatch). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_nonconvergence alignment_nonconvergence GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (alignment_nonconvergence). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_objective_not_evaluable alignment_objective_not_evaluable CONCLUSION Alignment invariance could not be evaluated (alignment_objective_not_evaluable). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_engine_error alignment_engine_error CONCLUSION Alignment invariance could not be evaluated (alignment_engine_error). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS alignment sentinel REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason constraint_engine_error constraint_engine_error GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (constraint_engine_error). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS constraint sentinel REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason lambda_list_parm_dif_nonfinite_or_empty lambda_list_parm_dif_nonfinite_or_empty GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (lambda_list_parm_dif_nonfinite_or_empty). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_objective_not_evaluable alignment_objective_not_evaluable GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (alignment_objective_not_evaluable). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_objective_not_evaluable alignment_objective_not_evaluable GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (alignment_objective_not_evaluable). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_objective_not_evaluable alignment_objective_not_evaluable GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (alignment_objective_not_evaluable). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_objective_out_of_range alignment_objective_out_of_range GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (alignment_objective_out_of_range). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.716 0.000 0.000 i1 0.796 0.000 0.000 i3 0.751 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason lambda_list_prop_noninvariance_out_of_range lambda_list_prop_noninvariance_out_of_range GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (lambda_list_prop_noninvariance_out_of_range). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason lambda_list_prop_noninvariance_out_of_range lambda_list_prop_noninvariance_out_of_range GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (lambda_list_prop_noninvariance_out_of_range). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason lambda_list_prop_noninvariance_inconsistent lambda_list_prop_noninvariance_inconsistent GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (lambda_list_prop_noninvariance_inconsistent). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason lambda_list_miss_items_not_binary lambda_list_miss_items_not_binary GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (lambda_list_miss_items_not_binary). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason lambda_list_miss_items_not_binary lambda_list_miss_items_not_binary GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Alignment invariance could not be evaluated (lambda_list_miss_items_not_binary). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason configural_engine_error configural_engine_error CONCLUSION Alignment invariance could not be evaluated (configural_engine_error). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS config sentinel REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason configural_nonconvergence configural_nonconvergence CONCLUSION Alignment invariance could not be evaluated (configural_nonconvergence). Do not interpret invariance percentages or R2 values. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible status Loadings - - 25.000 - not_evaluable Intercepts - - 25.000 - not_evaluable reason alignment_vcov_invalid alignment_vcov_invalid CONCLUSION Alignment invariance could not be evaluated (alignment_vcov_invalid). Do not interpret invariance percentages or R2 values. ANALYSIS ERRORS `vcov` must be positive semidefinite. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.00 0.00 25.00 TRUE Intercepts 0.95 0.00 25.00 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.72 0.00 0.00 i1 0.80 0.00 0.00 i3 0.75 0.00 0.00 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.01 0.00 0.00 i1 -0.02 0.00 0.00 i3 -0.00 0.00 0.00 GROUP PARAMETERS Group Latent mean Latent SD B 0.00 1.00 A 0.11 0.99 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 0.999852 0.000000 25.000000 TRUE Intercepts 0.952581 0.000000 25.000000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715321 0.000000 0.000000 i1 0.795765 0.000000 0.000000 i3 0.750469 0.000000 0.000000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.010851 0.000000 0.000000 i1 -0.017411 0.000000 0.000000 i3 -0.000236 0.000000 0.000000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000000 1.000000 A 0.107162 0.985434 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) i2 0.715 0.000 0.000 i1 0.796 0.000 0.000 i3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) i2 0.011 0.000 0.000 i1 -0.017 0.000 0.000 i3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD B 0.000 1.000 A 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 Report saved: /var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/file1609f1abbfda3.xlsx PsychoMatic data specification n = 4, items = 2 item measurement_level q1 continuous q2 continuous PsychoMatic item check severity n error 1 warning 0 info 0 ================================================================================ ITEM SCREENING ================================================================================ DESCRIPTIVES Item N Missing Missing (%) Mean SD Min Max q2 6 0.000 0.000 2.000 0.894 1.000 3.000 q1 6 0.000 0.000 2.667 1.633 1.000 5.000 DISTRIBUTION AND ENDPOINTS Item Skewness Kurtosis Categories Floor (%) Ceiling (%) q2 0.000 -1.958 3.000 33.300 33.300 q1 0.213 -1.865 5.000 33.300 16.700 ITEM CHECKS AND FLAGS Item Item-rest r No variance Floor Ceiling Review key q2 -0.274 No No No Yes q1 -0.274 No No No Yes ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.900 31 5 1 ok spearman 0.900 31 5 1 ok pearson 0.950 31 5 1 ok spearman 0.950 31 5 1 ok pearson 0.900 32 5 1 ok spearman 0.900 32 5 1 ok pearson 0.950 32 5 1 ok spearman 0.950 32 5 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 8.000 8.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.900 31 5 1 ok spearman 0.900 31 5 1 ok pearson 0.950 31 5 1 ok spearman 0.950 31 5 1 ok pearson 0.900 32 5 1 ok spearman 0.900 32 5 1 ok pearson 0.950 32 5 1 ok spearman 0.950 32 5 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 8.000 8.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.900 33 4 0 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 1.000 1.000 0.000 1.000 TRUE observed_solutions 0 CONCLUSION Evaluable configurations produced a descriptive range of 0 to 0 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.900 33 4 0 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 1.000 1.000 0.000 1.000 TRUE observed_solutions 0 CONCLUSION Evaluable configurations produced a descriptive range of 0 to 0 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason spearman 0.950 34 3 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 1.000 1.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.950 37 3 2 ok spearman 0.950 37 3 2 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 2.000 2.000 0.000 1.000 TRUE observed_solutions 2 CONCLUSION Evaluable configurations produced a descriptive range of 2 to 2 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason polychoric 0.950 35 3 1 ok spearman 0.950 35 3 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 2.000 2.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.950 36 3 1 ok spearman 0.950 36 3 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 2.000 2.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason polychoric 0.950 38 3 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 1.000 1.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason polychoric 0.950 41 3 1 ok spearman 0.950 41 3 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 2.000 2.000 0.000 1.000 TRUE observed_solutions 1 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 1 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason tetrachoric 0.950 42 3 3 ok pearson 0.950 42 3 1 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 2.000 2.000 0.000 2.000 FALSE observed_solutions 1, 3 CONCLUSION Evaluable configurations produced a descriptive range of 1 to 3 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status reason pearson 0.950 43 3 2 ok AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 1.000 1.000 0.000 1.000 TRUE observed_solutions 2 CONCLUSION Evaluable configurations produced a descriptive range of 2 to 2 factors; interpret sensitivity alongside theory and item quality. ================================================================================ DIMENSIONALITY SENSITIVITY ================================================================================ CONFIGURATIONS requested_method quantile seed n_iter n_factors status pearson 0.950 52 3 - skipped reason: The correlation matrix is not positive definite (minimum eigenvalue -3.3307e-16); repair was not requested. AGREEMENT n_configurations n_evaluable n_skipped n_distinct_solutions exact_agreement 1.000 0.000 1.000 0.000 FALSE observed_solutions CONCLUSION No configuration was evaluable; inspect the reason recorded for each cell. ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 90 Estimator: ML Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 45 g2 45 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 25.883 18 0.102 0.951 0.099 0.060 metric 29.318 23 0.170 0.961 0.078 0.079 scalar 33.299 28 0.225 0.967 0.065 0.086 strict 36.785 34 0.341 0.983 0.043 0.088 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.951 >= 0.9 Met RMSEA 0.099 <= 0.08 Not met SRMR 0.060 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 90 Estimator: ML Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 45 g2 45 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 25.883 18 0.102 0.951 0.099 0.060 metric 29.318 23 0.170 0.961 0.078 0.079 scalar 33.299 28 0.225 0.967 0.065 0.086 strict 36.785 34 0.341 0.983 0.043 0.088 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.951 >= 0.9 Met RMSEA 0.099 <= 0.08 Not met SRMR 0.060 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 160 Estimator: ML Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 80 g2 80 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 24.767 18 0.131 0.981 0.069 0.037 metric 28.220 23 0.208 0.985 0.053 0.051 scalar 30.941 28 0.320 0.992 0.036 0.054 strict 37.889 34 0.296 0.989 0.038 0.060 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - supported metric configural 0.004 -0.015 0.014 supported scalar metric 0.006 -0.017 0.003 supported strict scalar -0.003 0.002 0.006 supported CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.981 >= 0.9 Met RMSEA 0.069 <= 0.08 Met SRMR 0.037 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Fit-change heuristics were sequentially compatible through the 'strict' level. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 60 Estimator: MLR Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 30 g2 30 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural - - - - - - metric - - - - - - scalar - - - - - - strict - - - - - - CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_evaluable metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural not_evaluable metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: converged;post_check;finite_parameters;negative_observed_variance;nonfinite_cfi;nonfinite_rmsea;nonfinite_srmr;nonfinite_df 2. reason: converged;post_check;finite_parameters;nonfinite_cfi;nonfinite_rmsea;nonfinite_srmr;nonfinite_df CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI - >= 0.9 Not evaluable RMSEA - <= 0.08 Not evaluable SRMR - <= 0.08 Not evaluable CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. ANALYSIS ERRORS lavaan->lav_fit(): fit measures not available if model did not converge system is computationally singular: reciprocal condition number = 1.50439e-17 WARNINGS Mardia statistics are not evaluable because the population covariance matrix is singular: Lapack routine dgesv: system is exactly singular: U[6,6] = 0 lavaan->lav_mvn_mi_h1_est_moments(): The EM estimated variance-covariance matrix (Sigma) is (near) singular: its smallest eigenvalue is smaller than 1e-05. This may cause numerical instabilities; interpret the results with caution. lavaan->lav_step11_estoptim(): the optimizer warns that a solution has NOT been found! lavaan->lav_step15_baseline(): estimation of the baseline model failed. lavaan->lav_object_post_check(): some estimated ov variances are negative REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 70 Estimator: ULS Missing: two.stage Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 35 g2 35 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 3.580 18 - 1.000 0.000 0.052 metric 7.486 23 - 1.000 0.000 0.079 scalar 10.912 28 - 1.000 0.000 0.092 strict 18.776 34 - 1.000 0.000 0.121 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - supported metric configural 0.000 0.000 0.027 supported scalar metric 0.000 0.000 0.012 supported strict scalar 0.000 0.000 0.030 supported CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 1.000 >= 0.9 Met RMSEA 0.000 <= 0.08 Met SRMR 0.052 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Fit-change heuristics were sequentially compatible through the 'strict' level. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 68 Estimator: MLR Missing: listwise Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 34 g2 34 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 30.406 18 0.034 0.934 0.142 0.065 metric 38.595 23 0.022 0.918 0.141 0.115 scalar 42.734 28 0.037 0.922 0.124 0.122 strict 60.521 34 0.003 0.860 0.151 0.110 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.934 >= 0.9 Met RMSEA 0.142 <= 0.08 Not met SRMR 0.065 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. WARNINGS 2 cases were removed by the item missing-data policy. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 68 Estimator: MLR Missing: listwise Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 34 g2 34 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 30.406 18 0.034 0.934 0.142 0.065 metric 38.595 23 0.022 0.918 0.141 0.115 scalar 42.734 28 0.037 0.922 0.124 0.122 strict 60.521 34 0.003 0.860 0.151 0.110 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.934 >= 0.9 Met RMSEA 0.142 <= 0.08 Not met SRMR 0.065 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. WARNINGS 2 cases were removed by the item missing-data policy. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 68 Estimator: MLR Missing: listwise Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 34 g2 34 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 30.406 18 0.034 0.934 0.142 0.065 metric 38.595 23 0.022 0.918 0.141 0.115 scalar 42.734 28 0.037 0.922 0.124 0.122 strict 60.521 34 0.003 0.860 0.151 0.110 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.934 >= 0.9 Met RMSEA 0.142 <= 0.08 Not met SRMR 0.065 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. WARNINGS 2 cases were removed by the item missing-data policy. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 68 Estimator: MLR Missing: listwise Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 34 g2 34 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 30.406 18 0.034 0.934 0.142 0.065 metric 38.595 23 0.022 0.918 0.141 0.115 scalar 42.734 28 0.037 0.922 0.124 0.122 strict 60.521 34 0.003 0.860 0.151 0.110 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.934 >= 0.9 Met RMSEA 0.142 <= 0.08 Not met SRMR 0.065 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. WARNINGS 2 cases were removed by the item missing-data policy. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 50 Estimator: ML Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 25 g2 25 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 26.329 18 0.092 0.919 0.136 0.072 metric 26.769 23 0.266 0.964 0.081 0.076 scalar 28.987 28 0.413 0.990 0.038 0.082 strict 30.669 34 0.632 1.000 0.000 0.085 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.919 >= 0.9 Met RMSEA 0.136 <= 0.08 Not met SRMR 0.072 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 49 Estimator: ML Missing: listwise Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 24 g2 25 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 23.136 18 0.185 0.960 0.108 0.053 metric 25.450 23 0.327 0.981 0.066 0.083 scalar 30.864 28 0.323 0.978 0.065 0.094 strict 37.711 34 0.303 0.971 0.067 0.115 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.960 >= 0.9 Met RMSEA 0.108 <= 0.08 Not met SRMR 0.053 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. WARNINGS 1 cases with missing group membership were removed. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 40 Estimator: ML Missing: listwise Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 20 g2 20 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 25.511 18 0.111 0.922 0.144 0.078 metric 37.545 23 0.028 0.848 0.178 0.163 scalar 39.425 28 0.074 0.881 0.143 0.166 strict 56.776 34 0.008 0.762 0.183 0.213 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.922 >= 0.9 Met RMSEA 0.144 <= 0.08 Not met SRMR 0.078 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. WARNINGS 20 cases were removed by the item missing-data policy. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 50 Estimator: MLR Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N 1 25 2 25 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 29.033 18 0.048 0.900 0.157 0.066 metric 33.422 23 0.074 0.905 0.135 0.107 scalar 38.457 28 0.090 0.905 0.122 0.120 strict 43.034 34 0.138 0.918 0.103 0.129 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.900 >= 0.9 Not met RMSEA 0.157 <= 0.08 Not met SRMR 0.066 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 50 Estimator: MLR Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 25 g2 25 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 29.033 18 0.048 0.900 0.157 0.066 metric 33.422 23 0.074 0.905 0.135 0.107 scalar 38.457 28 0.090 0.905 0.122 0.120 strict 43.034 34 0.138 0.918 0.103 0.129 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - not_supported metric configural - - - not_evaluable scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status configural Insufficient configural fit metric not_evaluable scalar not_evaluable strict not_evaluable REASONS 1. reason: At least one configural fit criterion was not met; see Configural evaluation. 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.900 >= 0.9 Not met RMSEA 0.157 <= 0.08 Not met SRMR 0.066 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Configural evidence was insufficient or not evaluable; later invariance levels must not be interpreted. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 70 Estimator: MLR Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 35 g2 35 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 19.133 18 0.384 0.995 0.042 0.045 metric 29.303 23 0.170 0.970 0.088 0.109 scalar 33.499 28 0.218 0.974 0.075 0.115 strict 39.133 34 0.250 0.976 0.066 0.113 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - supported metric configural -0.024 0.046 0.064 not_supported scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status scalar not_evaluable strict not_evaluable REASONS reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.995 >= 0.9 Met RMSEA 0.042 <= 0.08 Met SRMR 0.045 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Fit-change heuristics were sequentially compatible through the 'configural' level. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 70 Estimator: MLR Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 35 g2 35 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 19.133 18 0.384 0.995 0.042 0.045 metric 29.303 23 0.170 0.970 0.088 0.109 scalar 33.499 28 0.218 0.974 0.075 0.115 strict 39.133 34 0.250 0.976 0.066 0.113 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - supported metric configural - - - not_supported scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status metric skipped_not_identified scalar not_evaluable strict not_evaluable REASONS 1. reason: fit_deterioration_exceeded_the_joint_heuristic 2. reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.995 >= 0.9 Met RMSEA 0.042 <= 0.08 Met SRMR 0.045 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Fit-change heuristics were sequentially compatible through the 'configural' level. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 Report saved: /var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/file1609f1544fa0d.xlsx ================================================================================ MEASUREMENT INVARIANCE ================================================================================ DATA AND METHOD Response options (observed): 70 Estimator: ML Missing: fiml Criteria: chen_informed_guidelines FIT-INDEX VARIANT CFI / RMSEA: scaled (base for uncorrected estimators with the default variant). Chi-square, df and p: scaled for corrected estimators; SRMR: base. Unavailable requested indices are not substituted. METHOD AND INTERPRETATION Reproduces native lavaan calls with four stages: configural, equal loadings (metric), equal loadings and intercepts (scalar), and equal loadings, intercepts and residuals (strict). WLSMV/ULSMV default to ordered responses, marker identification and delta parameterization. ML/MLR/ULS analyze numeric scores. With ordinal data these labels do not guarantee independent comparisons; ordinal_invariance_auto() implements the identified threshold/loading sequence. SAMPLE BY GROUP Group N g1 35 g2 35 FIT BY STAGE Stage Chi-square df p CFI RMSEA SRMR configural 19.604 18 0.356 0.992 0.050 0.045 metric 28.202 23 0.208 0.974 0.080 0.109 scalar 32.344 28 0.261 0.978 0.067 0.115 strict 37.606 34 0.307 0.982 0.055 0.113 CHANGES AND DECISIONS level comparison_from ΔCFI ΔRMSEA ΔSRMR decision configural - - - - supported metric configural -0.018 0.030 0.064 not_supported scalar metric - - - not_evaluable strict scalar - - - not_evaluable NON-EVALUABLE STAGES level status scalar not_evaluable strict not_evaluable REASONS reason: A less restrictive stage was not supported; this comparison is not interpreted. CONFIGURAL EVALUATION Index Value Criterion Evaluation CFI 0.992 >= 0.9 Met RMSEA 0.050 <= 0.08 Met SRMR 0.045 <= 0.08 Met CHANGE CUTOFFS Index Value CFI decrease 0.010 RMSEA increase 0.015 SRMR increase: metric 0.030 SRMR increase: other 0.010 JOINT DECISION RULE Invariance is not supported when the CFI decrease exceeds its cutoff AND either the RMSEA or SRMR increase exceeds its cutoff. An unsupported earlier stage prevents favorable interpretation of later stages. CONCLUSION Fit-change heuristics were sequentially compatible through the 'configural' level. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: scalar Status: not_evaluable Measurement: continuous Estimator: NA Workflow: factorial Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS input_order family lhs op rhs canonical 1.000 intercepts i3 ~1 i3 ~ 1 rationale matched_groups equality_in_full A preregistered intercept hypothesis. - - effective_release release_reason FALSE not_attempted_configural_failure RATIONALE input_order canonical rationale 1.000 i3 ~ 1 A preregistered intercept hypothesis. COMPARISONS comparison comparable reason delta_df full_prerequisite_vs_full FALSE configural_fit_not_evaluable - prerequisite_vs_partial FALSE configural_fit_not_evaluable - full_vs_partial_diagnostic FALSE configural_fit_not_evaluable - ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea improvement_srmr - - - - - - - - - - - - - - - - - - cfi_variant rmsea_variant srmr_variant decision - - - not_evaluable - - - not_evaluable - - - - decision_reason configural_fit_not_evaluable configural_fit_not_evaluable - FIT role chi2 df p cfi rmsea srmr configural - - - - - - CONCLUSION Required evidence was not evaluable; inspect fits, admissibility, constraints, and diagnostics. ANALYSIS ERRORS simulated configural engine failure REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: scalar Status: partial_invariance_supported Measurement: continuous Estimator: ML Workflow: factorial Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs i3 ~ 1 1.000 intercepts i3 ~1 rationale matched_groups equality_in_full A preregistered intercept hypothesis. g1, g2 TRUE effective_release release_reason TRUE requested_equality_family_released RATIONALE input_order canonical rationale 1.000 i3 ~ 1 A preregistered intercept hypothesis. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE i3 ~ 1 f i4 TRUE f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic TRUE same_stage_partial_to_full_diagnostic delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea 5.000 -0.047 0.038 0.020 - - 4.000 0.008 -0.017 0.000 - - 1.000 - - - 0.055 0.055 improvement_srmr cfi_variant rmsea_variant srmr_variant decision - base base base not_supported - base base base supported 0.020 base base base - 1. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 2. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 13.119 18 0.784 1.000 0.000 0.027 prerequisite_full 32.090 23 0.098 0.977 0.066 0.097 prerequisite_matched 32.090 23 0.098 0.977 0.066 0.097 full 55.272 28 0.002 0.930 0.104 0.117 partial 32.853 27 0.202 0.985 0.049 0.097 CONCLUSION The partial-invariance stage was compatible with the fit-change heuristics using the justified releases. This is not proof of invariance and requires substantive judgment. WARNINGS 1 cases with missing group membership were removed. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: scalar Status: partial_invariance_not_supported Measurement: continuous Estimator: ML Workflow: factorial Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs rationale f =~ i3 1.000 loadings f =~ i3 Prior loading evidence. matched_groups equality_in_full effective_release g1, g2 TRUE TRUE release_reason requested_equality_family_released RATIONALE input_order canonical rationale 1.000 f =~ i3 Prior loading evidence. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE f =~ i3 f i4 TRUE f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic TRUE same_stage_partial_to_full_diagnostic delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea 5.000 -0.025 0.013 0.013 - - 5.000 -0.015 0.054 0.035 - - 1.000 - - - 0.053 0.059 improvement_srmr cfi_variant rmsea_variant srmr_variant decision - base base base not_supported - base base base not_supported 0.058 base base base - 1. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 2. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 11.572 18 0.869 1.000 0.000 0.021 prerequisite_full 43.650 23 0.006 0.956 0.100 0.127 prerequisite_matched 15.868 22 0.822 1.000 0.000 0.046 full 60.376 28 <0.001 0.931 0.113 0.140 partial 34.215 27 0.160 0.985 0.054 0.082 CONCLUSION The partial-invariance stage was not compatible with the fit-change heuristics; do not add automated releases without independent justification. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: loadings Status: partial_invariance_not_supported Measurement: ordinal Estimator: WLSMV Workflow: ordinal Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs rationale f =~ i3 1.000 loadings f =~ i3 Prior ordinal loading evidence. matched_groups equality_in_full effective_release g1, g2 TRUE TRUE release_reason requested_equality_family_released RATIONALE input_order canonical rationale 1.000 f =~ i3 Prior ordinal loading evidence. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE f =~ i3 f i4 TRUE f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic TRUE same_stage_partial_to_full_diagnostic delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea 5.000 -0.013 0.018 0.010 - - 4.000 -0.011 0.017 0.007 - - 1.000 - - - 0.001 0.001 improvement_srmr cfi_variant rmsea_variant srmr_variant decision - scaled scaled base not_supported - scaled scaled base not_supported 0.002 scaled scaled base - 1. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 2. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 21.481 18 0.256 0.995 0.040 0.043 prerequisite_full 36.271 30 0.199 0.991 0.042 0.043 prerequisite_matched 36.271 30 0.199 0.991 0.042 0.043 full 50.001 35 0.048 0.978 0.060 0.053 partial 48.105 34 0.055 0.979 0.059 0.050 CONCLUSION The partial-invariance stage was not compatible with the fit-change heuristics; do not add automated releases without independent justification. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: strict Status: full_invariance_supported_partial_not_needed Measurement: ordinal Estimator: WLSMV Workflow: ordinal Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs matched_groups equality_in_full i3 | t2 1.000 thresholds i3 | t2 g1, g2 TRUE i4 ~~ i4 2.000 residuals i4 ~~ i4 g1, g2 TRUE effective_release release_reason TRUE requested_equality_family_released TRUE requested_equality_family_released 1. rationale: The two preregistered item parameters may differ by group. 2. rationale: The two preregistered item parameters may differ by group. RATIONALE input_order canonical 1.000 i3 | t2 2.000 i4 ~~ i4 1. rationale: The two preregistered item parameters may differ by group. 2. rationale: The two preregistered item parameters may differ by group. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE i3 | t2 f i4 FALSE i4 ~~ i4 f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic TRUE same_stage_partial_to_full_diagnostic delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea 6.000 0.003 -0.010 0.005 - - 5.000 -0.001 -0.004 0.009 - - 2.000 - - - 0.009 0.006 improvement_srmr cfi_variant rmsea_variant srmr_variant decision - scaled scaled base supported - scaled scaled base supported 0.001 scaled scaled base - 1. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 2. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 17.138 18 0.514 1.000 0.000 0.024 prerequisite_full 141.572 40 <0.001 0.939 0.108 0.039 prerequisite_matched 117.799 39 <0.001 0.953 0.096 0.034 full 142.079 46 <0.001 0.942 0.098 0.044 partial 125.147 44 <0.001 0.951 0.092 0.043 CONCLUSION Full invariance at the requested stage was compatible with the fit-change heuristics; the partial release was not needed. This is not formal proof of invariance. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: loadings Status: partial_invariance_supported Measurement: mixed Estimator: WLSMV Workflow: ordinal Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs matched_groups equality_in_full f =~ i3 1.000 loadings f =~ i3 g1, g2 TRUE effective_release release_reason TRUE requested_equality_family_released rationale: A preregistered mixed-indicator loading hypothesis. RATIONALE input_order canonical 1.000 f =~ i3 rationale: A preregistered mixed-indicator loading hypothesis. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE f =~ i3 f i4 TRUE f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic TRUE same_stage_partial_to_full_diagnostic delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea 5.000 -0.056 0.085 0.022 - - 4.000 -0.001 0.010 0.007 - - 1.000 - - - 0.055 0.075 improvement_srmr cfi_variant rmsea_variant srmr_variant decision - scaled scaled base not_supported - scaled scaled base supported 0.016 scaled scaled base - 1. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 2. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 16.050 18 0.589 1.000 0.000 0.027 prerequisite_full 20.345 21 0.500 1.000 0.000 0.027 prerequisite_matched 20.345 21 0.500 1.000 0.000 0.027 full 67.387 26 <0.001 0.944 0.085 0.049 partial 25.561 25 0.431 0.999 0.010 0.033 CONCLUSION The partial-invariance stage was compatible with the fit-change heuristics using the justified releases. This is not proof of invariance and requires substantive judgment. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: scalar Status: full_invariance_supported_partial_not_needed Measurement: ordinal Estimator: WLSMV Workflow: ordinal Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs i3 | t1 1.000 thresholds i3 | t1 rationale matched_groups equality_in_full A preregistered binary-threshold hypothesis. g1, g2 TRUE effective_release release_reason TRUE requested_equality_family_released RATIONALE input_order canonical rationale 1.000 i3 | t1 A preregistered binary-threshold hypothesis. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE i3 | t1 f i4 TRUE f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic FALSE full_minus_partial_df_not_positive delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea improvement_srmr 4.000 0.000 0.000 0.000 - - - 4.000 0.000 0.000 0.000 - - - 0.000 - - - - - - cfi_variant rmsea_variant srmr_variant decision scaled scaled base supported scaled scaled base supported - - - - 1. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 2. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 9.761 18 0.939 1.000 0.000 0.020 prerequisite_full 9.761 18 0.939 1.000 0.000 0.020 prerequisite_matched 9.761 18 0.939 1.000 0.000 0.020 full 19.994 22 0.583 1.000 0.000 0.020 partial 15.963 22 0.818 1.000 0.000 0.020 CONCLUSION Full invariance at the requested stage was compatible with the fit-change heuristics; the partial release was not needed. This is not formal proof of invariance. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 Report saved: /var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/partial-invariance-1609f51f68789.xlsx ================================================================================ PARTIAL INVARIANCE ================================================================================ DATA AND METHOD Stage: scalar Status: partial_invariance_supported Measurement: continuous Estimator: ML Workflow: factorial Fit_variant: scaled SELECTED INDICES CFI and RMSEA use the requested variant; chi-square, df and p use scaled when applicable and SRMR uses base. For uncorrected estimators, scaled uses base indices. Unavailable robust indices are not substituted. RELEASED PARAMETERS canonical input_order family lhs op rhs rationale matched_groups i3 ~ 1 1.000 intercepts i3 ~1 Theory. g1, g2 equality_in_full effective_release release_reason TRUE TRUE requested_equality_family_released RATIONALE input_order canonical rationale 1.000 i3 ~ 1 Theory. ANCHORS factor item retained released_by f i1 TRUE f i2 TRUE f i3 FALSE i3 ~ 1 f i4 TRUE f i5 TRUE f i6 TRUE COMPARISONS comparison comparable reason full_prerequisite_vs_full TRUE comparable prerequisite_vs_partial TRUE comparable full_vs_partial_diagnostic TRUE same_stage_partial_to_full_diagnostic delta_df ΔCFI ΔRMSEA ΔSRMR improvement_cfi improvement_rmsea 5.000 -0.020 0.011 0.012 - - 4.000 0.004 -0.010 0.003 - - 1.000 - - - 0.024 0.022 improvement_srmr cfi_variant rmsea_variant srmr_variant decision - base base base not_supported - base base base supported 0.010 base base base - 1. decision_reason: fit_deterioration_exceeded_the_joint_heuristic 2. decision_reason: fit_deterioration_remained_within_the_joint_heuristic 3. decision_reason: - FIT role chi2 df p cfi rmsea srmr configural 26.067 18 0.098 0.979 0.071 0.037 prerequisite_full 36.713 23 0.035 0.965 0.081 0.082 prerequisite_matched 36.713 23 0.035 0.965 0.081 0.082 full 49.670 28 0.007 0.945 0.093 0.094 partial 39.316 27 0.059 0.969 0.071 0.084 CONCLUSION The partial-invariance stage was compatible with the fit-change heuristics using the justified releases. This is not proof of invariance and requires substantive judgment. REFERENCES Bowen, N. K., & Masa, R. D. (2015). Conducting measurement invariance tests with ordinal data: A guide for social work researchers. Journal of the Society for Social Work and Research, 6(2), 229-249. https://doi.org/10.1086/681607 Chen, F. F. (2007). Sensitivity of goodness of fit indexes to lack of measurement invariance. Structural Equation Modeling: A Multidisciplinary Journal, 14(3), 464-504. https://doi.org/10.1080/10705510701301834 Hirschfeld, G., & von Brachel, R. (2014). Multiple-group confirmatory factor analysis in R: A tutorial in measurement invariance with continuous and ordinal indicators. Practical Assessment, Research & Evaluation, 19, Article 7. https://doi.org/10.7275/qazy-2946 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1-36. https://doi.org/10.18637/jss.v048.i02 Wu, H., & Estabrook, R. (2016). Identification of confirmatory factor analysis models of different levels of invariance for ordered categorical outcomes. Psychometrika, 81(4), 1014-1045. https://doi.org/10.1007/s11336-016-9506-0 Saving _problems/test-invariance-partial-911.R ================================================================================ ITEM RESPONSE THEORY ================================================================================ MODEL SUMMARY model itemtype n n_items items_to_review mean_discrimination 2pl 2PL 40 0 0.000 - recommendation: Model not evaluable: Too few degrees of freedom. There are only 3 degrees of freedom but 4 parameters were freely estimated. CONCLUSION Too few degrees of freedom. There are only 3 degrees of freedom but 4 parameters were freely estimated. ANALYSIS ERRORS Too few degrees of freedom. There are only 3 degrees of freedom but 4 parameters were freely estimated. REFERENCES Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573. https://doi.org/10.1007/BF02293814 Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29-51. https://doi.org/10.1007/BF02291411 Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459. https://doi.org/10.1007/BF02293801 Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. https://doi.org/10.18637/jss.v048.i06 Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176. https://doi.org/10.1177/014662169201600206 ================================================================================ ITEM RESPONSE THEORY ================================================================================ MODEL SUMMARY model itemtype n n_items items_to_review mean_discrimination 2pl 2PL 240 4 1.000 0.813 recommendation: Few items require review; prioritize content, discrimination, and thresholds. ITEM PARAMETERS item a1 d g u discrimination_magnitude a b i1 1.115 -0.147 0.000 1.000 1.115 1.115 0.132 i2 0.483 0.035 0.000 1.000 0.483 0.483 -0.073 i3 0.898 -0.236 0.000 1.000 0.898 0.898 0.263 i4 0.757 0.245 0.000 1.000 0.757 0.757 -0.323 INTERPRETATION item discrimination discrimination_level difficulty_center threshold_min i1 1.115 Moderate 0.132 0.132 i2 0.483 Low -0.073 -0.073 i3 0.898 Moderate 0.263 0.263 i4 0.757 Moderate -0.323 -0.323 threshold_max threshold_ordered 0.132 TRUE -0.073 TRUE 0.263 TRUE -0.323 TRUE 1. recommendation: No major flag; review together with item content and test information. 2. recommendation: Review item for low discrimination . 3. recommendation: No major flag; review together with item content and test information. 4. recommendation: No major flag; review together with item content and test information. REFERENCES Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573. https://doi.org/10.1007/BF02293814 Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29-51. https://doi.org/10.1007/BF02291411 Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459. https://doi.org/10.1007/BF02293801 Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. https://doi.org/10.18637/jss.v048.i06 Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176. https://doi.org/10.1177/014662169201600206 ================================================================================ ITEM RESPONSE THEORY ================================================================================ MODEL SUMMARY model itemtype n n_items items_to_review mean_discrimination 2pl 2PL 240 4 1.0000000 0.8133567 recommendation: Few items require review; prioritize content, discrimination, and thresholds. ITEM PARAMETERS item a1 d g u discrimination_magnitude i1 1.1147475 -0.1472898 0.0000000 1.0000000 1.1147475 i2 0.4834901 0.0351210 0.0000000 1.0000000 0.4834901 i3 0.8978367 -0.2360109 0.0000000 1.0000000 0.8978367 i4 0.7573524 0.2449357 0.0000000 1.0000000 0.7573524 a b 1.1147475 0.1321284 0.4834901 -0.0726405 0.8978367 0.2628662 0.7573524 -0.3234105 INTERPRETATION item discrimination discrimination_level difficulty_center threshold_min i1 1.1147475 Moderate 0.1321284 0.1321284 i2 0.4834901 Low -0.0726405 -0.0726405 i3 0.8978367 Moderate 0.2628662 0.2628662 i4 0.7573524 Moderate -0.3234105 -0.3234105 threshold_max threshold_ordered 0.1321284 TRUE -0.0726405 TRUE 0.2628662 TRUE -0.3234105 TRUE 1. recommendation: No major flag; review together with item content and test information. 2. recommendation: Review item for low discrimination . 3. recommendation: No major flag; review together with item content and test information. 4. recommendation: No major flag; review together with item content and test information. REFERENCES Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573. https://doi.org/10.1007/BF02293814 Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29-51. https://doi.org/10.1007/BF02291411 Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459. https://doi.org/10.1007/BF02293801 Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. https://doi.org/10.18637/jss.v048.i06 Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176. https://doi.org/10.1177/014662169201600206 ================================================================================ ITEM RESPONSE THEORY ================================================================================ MODEL SUMMARY model itemtype n n_items items_to_review mean_discrimination mixed 2PL, graded 600 8 0.000 1.060 recommendation: No major item flags; review item content and test information before concluding. ITEM PARAMETERS item a1 d g u d1 d2 d3 discrimination_magnitude i1 0.758 -0.204 0.000 1.000 - - - 0.758 i2 0.953 0.032 0.000 1.000 - - - 0.953 i3 1.105 0.200 0.000 1.000 - - - 1.105 i4 1.298 0.266 0.000 1.000 - - - 1.298 i5 1.007 - - - 0.608 -0.218 -0.980 1.007 i6 1.072 - - - 0.814 -0.182 -1.022 1.072 i7 1.108 - - - 0.792 -0.101 -0.825 1.108 i8 1.182 - - - 0.833 0.062 -0.713 1.182 a b b1 b2 b3 0.758 0.269 - - - 0.953 -0.033 - - - 1.105 -0.181 - - - 1.298 -0.205 - - - 1.007 - -0.604 0.217 0.974 1.072 - -0.759 0.170 0.953 1.108 - -0.715 0.092 0.744 1.182 - -0.705 -0.052 0.603 INTERPRETATION item discrimination discrimination_level difficulty_center threshold_min i1 0.758 Moderate 0.269 0.269 i2 0.953 Moderate -0.033 -0.033 i3 1.105 Moderate -0.181 -0.181 i4 1.298 Moderate -0.205 -0.205 i5 1.007 Moderate 0.196 -0.604 i6 1.072 Moderate 0.121 -0.759 i7 1.108 Moderate 0.040 -0.715 i8 1.182 Moderate -0.051 -0.705 threshold_max threshold_ordered 0.269 TRUE -0.033 TRUE -0.181 TRUE -0.205 TRUE 0.974 TRUE 0.953 TRUE 0.744 TRUE 0.603 TRUE 1. recommendation: No major flag; review together with item content and test information. 2. recommendation: No major flag; review together with item content and test information. 3. recommendation: No major flag; review together with item content and test information. 4. recommendation: No major flag; review together with item content and test information. 5. recommendation: No major flag; review together with item content and test information. 6. recommendation: No major flag; review together with item content and test information. 7. recommendation: No major flag; review together with item content and test information. 8. recommendation: No major flag; review together with item content and test information. REFERENCES Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573. https://doi.org/10.1007/BF02293814 Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29-51. https://doi.org/10.1007/BF02291411 Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459. https://doi.org/10.1007/BF02293801 Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. https://doi.org/10.18637/jss.v048.i06 Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176. https://doi.org/10.1177/014662169201600206 ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 4 1.000 0.000 1.000 0.000 flagged_pct alpha groups 0.250 0.050 A, B recommendation: Few items show possible DIF; review those items before deletion or adjustment decisions. ITEM RESULTS item p_uniform p_nonuniform effect_size status reason focal 0.212 0.183 0.006 evaluable - r1 0.848 0.011 0.022 evaluable - r2 0.327 0.277 0.004 evaluable - r3 0.404 0.144 0.008 evaluable - INTERPRETATION item dif_type severity focal none no_flag r1 nonuniform review r2 none no_flag r3 none no_flag 1. decision: No statistical DIF evidence in this screening. 1. recommendation: Retain unless theory or substantive evidence suggests review. 2. decision: Possible nonuniform DIF. 2. recommendation: Review item-by-group interaction and consider ordinal or IRT DIF follow-up. 3. decision: No statistical DIF evidence in this screening. 3. recommendation: Retain unless theory or substantive evidence suggests review. 4. decision: No statistical DIF evidence in this screening. 4. recommendation: Retain unless theory or substantive evidence suggests review. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 0.000 0.000 0.000 2.000 flagged_pct alpha groups 0.000 0.050 A, B recommendation: 2 item(s) were not evaluable; absence of flags must not be interpreted as equivalent item functioning. ITEM RESULTS item p_uniform p_nonuniform effect_size status constant - - - not_evaluable varying 1.000 1.000 0.000 evaluable poly - - - not_evaluable 1. reason: `constant` is constant. 2. reason: - 3. reason: Polytomous or ordinal items require a dedicated ordinal or IRT DIF method. INTERPRETATION item dif_type severity constant not_evaluable not_evaluable varying none no_flag poly not_evaluable not_evaluable 1. decision: Not assessable with this screening. 1. recommendation: Increase variation or sample size before interpreting. `constant` is constant. 2. decision: No statistical DIF evidence in this screening. 2. recommendation: Retain unless theory or substantive evidence suggests review. 3. decision: Not assessable with this screening. 3. recommendation: Increase variation or sample size before interpreting. Polytomous or ordinal items require a dedicated ordinal or IRT DIF method. CONCLUSION One or more requested items were not evaluable; inspect item-level reasons. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 2 0.000 0.000 0.000 1.000 flagged_pct alpha groups 0.000 0.010 A, B recommendation: 1 item(s) were not evaluable; absence of flags must not be interpreted as equivalent item functioning. ITEM RESULTS item p_uniform p_nonuniform effect_size status poly - - - not_evaluable varying 1.000 1.000 0.000 evaluable 1. reason: The LR comparison was nonfinite or not correctly nested. 2. reason: - INTERPRETATION item dif_type severity poly not_evaluable not_evaluable varying none no_flag 1. decision: Not assessable with this screening. 1. recommendation: Increase variation or sample size before interpreting. Methodological warning: the polytomous item was median-dichotomized; confirm with a dedicated ordinal or IRT DIF method. 2. decision: No statistical DIF evidence in this screening. 2. recommendation: Retain unless theory or substantive evidence suggests review. CONCLUSION One or more requested items were not evaluable; inspect item-level reasons. WARNINGS Polytomous items were median-dichotomized for compatibility; confirm any DIF finding with a dedicated ordinal or IRT method. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 0.000 0.000 0.000 0.000 flagged_pct alpha groups 0.000 0.010 A, B recommendation: No DIF-flagged items in this screening; interpret together with theory and external evidence. ITEM RESULTS item p_uniform p_nonuniform effect_size status reason i1 0.713 0.204 0.009 evaluable - i2 0.287 0.794 0.006 evaluable - i3 0.912 0.215 0.008 evaluable - INTERPRETATION item dif_type severity i1 none no_flag i2 none no_flag i3 none no_flag 1. decision: No statistical DIF evidence in this screening. 1. recommendation: Retain unless theory or substantive evidence suggests review. 2. decision: No statistical DIF evidence in this screening. 2. recommendation: Retain unless theory or substantive evidence suggests review. 3. decision: No statistical DIF evidence in this screening. 3. recommendation: Retain unless theory or substantive evidence suggests review. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 0.000 0.000 0.000 0.000 flagged_pct alpha groups 0.000 0.010 A, B recommendation: No DIF-flagged items in this screening; interpret together with theory and external evidence. ITEM RESULTS item p_uniform p_nonuniform effect_size status reason i1 0.713 0.204 0.009 evaluable - i2 0.287 0.794 0.006 evaluable - i3 0.912 0.215 0.008 evaluable - INTERPRETATION item dif_type severity i1 none no_flag i2 none no_flag i3 none no_flag 1. decision: No statistical DIF evidence in this screening. 1. recommendation: Retain unless theory or substantive evidence suggests review. 2. decision: No statistical DIF evidence in this screening. 2. recommendation: Retain unless theory or substantive evidence suggests review. 3. decision: No statistical DIF evidence in this screening. 3. recommendation: Retain unless theory or substantive evidence suggests review. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 1 0.000 0.000 0.000 1.000 flagged_pct alpha groups 0.000 0.010 A, B recommendation: 1 item(s) were not evaluable; absence of flags must not be interpreted as equivalent item functioning. ITEM RESULTS item p_uniform p_nonuniform effect_size status i1 - - - not_evaluable reason: No usable rest item was available for a focal-excluded matching score. INTERPRETATION item dif_type decision severity i1 not_evaluable Not assessable with this screening. not_evaluable recommendation: Increase variation or sample size before interpreting. CONCLUSION One or more requested items were not evaluable; inspect item-level reasons. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 2 0.000 0.000 0.000 2.000 flagged_pct alpha groups 0.000 0.010 A, B recommendation: 2 item(s) were not evaluable; absence of flags must not be interpreted as equivalent item functioning. ITEM RESULTS item p_uniform p_nonuniform effect_size status i1 - - - not_evaluable i2 - - - not_evaluable 1. reason: At least one operational group has fewer than 10 usable observations. 2. reason: At least one operational group has fewer than 10 usable observations. INTERPRETATION item dif_type decision severity i1 not_evaluable Not assessable with this screening. not_evaluable i2 not_evaluable Not assessable with this screening. not_evaluable 1. recommendation: Increase variation or sample size before interpreting. 2. recommendation: Increase variation or sample size before interpreting. CONCLUSION One or more requested items were not evaluable; inspect item-level reasons. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 0.000 0.000 0.000 3.000 flagged_pct alpha groups 0.000 0.010 A, B recommendation: 3 item(s) were not evaluable; absence of flags must not be interpreted as equivalent item functioning. ITEM RESULTS item p_uniform p_nonuniform effect_size status focal - - - not_evaluable r1 - - - not_evaluable r2 - - - not_evaluable 1. reason: The logistic DIF solution contains a singular or nonfinite coefficient or likelihood. 2. reason: The logistic DIF solution contains a singular or nonfinite coefficient or likelihood. 3. reason: The logistic DIF solution contains a singular or nonfinite coefficient or likelihood. INTERPRETATION item dif_type decision severity focal not_evaluable Not assessable with this screening. not_evaluable r1 not_evaluable Not assessable with this screening. not_evaluable r2 not_evaluable Not assessable with this screening. not_evaluable 1. recommendation: Increase variation or sample size before interpreting. 2. recommendation: Increase variation or sample size before interpreting. 3. recommendation: Increase variation or sample size before interpreting. CONCLUSION One or more requested items were not evaluable; inspect item-level reasons. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 0.00 0.00 0.00 0.00 flagged_pct alpha groups 0.00 0.01 A, B recommendation: No DIF-flagged items in this screening; interpret together with theory and external evidence. ITEM RESULTS item p_uniform p_nonuniform effect_size status reason i1 0.39 0.22 0.01 evaluable - i2 0.79 0.56 0.00 evaluable - i3 0.18 0.34 0.01 evaluable - INTERPRETATION item dif_type severity i1 none no_flag i2 none no_flag i3 none no_flag 1. decision: No statistical DIF evidence in this screening. 1. recommendation: Retain unless theory or substantive evidence suggests review. 2. decision: No statistical DIF evidence in this screening. 2. recommendation: Retain unless theory or substantive evidence suggests review. 3. decision: No statistical DIF evidence in this screening. 3. recommendation: Retain unless theory or substantive evidence suggests review. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 0.0000000 0.0000000 0.0000000 0.0000000 flagged_pct alpha groups 0.0000000 0.0100000 A, B recommendation: No DIF-flagged items in this screening; interpret together with theory and external evidence. ITEM RESULTS item p_uniform p_nonuniform effect_size status reason i1 0.3926677 0.2172559 0.0063721 evaluable - i2 0.7916716 0.5628565 0.0014372 evaluable - i3 0.1787361 0.3432855 0.0076148 evaluable - INTERPRETATION item dif_type severity i1 none no_flag i2 none no_flag i3 none no_flag 1. decision: No statistical DIF evidence in this screening. 1. recommendation: Retain unless theory or substantive evidence suggests review. 2. decision: No statistical DIF evidence in this screening. 2. recommendation: Retain unless theory or substantive evidence suggests review. 3. decision: No statistical DIF evidence in this screening. 3. recommendation: Retain unless theory or substantive evidence suggests review. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic duplicate 0.856 0.760 0.187 0.114 5143.372 5187.857 duplicate 0.975 0.953 0.082 0.047 5066.503 5114.696 status evaluable evaluable RECOMMENDATION Model `duplicate` has the most favorable descriptive combination of higher CFI/TLI and lower RMSEA/SRMR; interpret this recommendation together with theory, loadings, and residuals. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic invalid_fit - - - - - - valid_fit 0.856 0.760 0.187 0.114 - - status not_evaluable evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. ANALYSIS ERRORS lavaan->lav_step02_options(): missing observed variables in dataset: absent1 absent2 absent3 ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic status a 1.000 1.000 0.000 0.000 - - evaluable b 1.000 1.000 0.000 0.000 - - evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic status a 1.000 1.000 0.000 0.000 - - evaluable b 1.000 1.000 0.000 0.000 - - evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic first 1.000 1.000 0.000 0.000 2725.955 2748.197 reordered 1.000 1.000 0.000 0.000 2725.955 2748.197 other 1.000 1.000 0.000 0.000 - - status evaluable evaluable evaluable RECOMMENDATION The best models tie on every available criterion; no positional recommendation is issued. CONCLUSION The best models tie on every available criterion; no positional recommendation is issued. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 240 Estimator: WLSMV Selection: User RATIONALE Estimator specified by the user FIT model CFI (scaled) TLI (scaled) RMSEA (scaled) SRMR (base) aic bic one 1.000 5.548 0.000 0.041 - - two 1.000 5.421 0.000 0.040 - - status evaluable not_evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. WARNINGS lavaan->lavaan(): the first indicator (the marker item) of the following latent variable(s) is a poor item (low corrected item-total correlation); this may lead to convergence problems; consider using a better indicator to set the metric, or set bad_marker_switch = TRUE to let lavaan switch the marker automatically (bad_marker_crit = 0 disables this check): f (i1, r = 0.10) lavaan->lavaan(): the first indicator (the marker item) of the following latent variable(s) is a poor item (low corrected item-total correlation); this may lead to convergence problems; consider using a better indicator to set the metric, or set bad_marker_switch = TRUE to let lavaan switch the marker automatically (bad_marker_crit = 0 disables this check): f1 (i1, r = -0.06) lavaan->lav_object_post_check(): some estimated lv variances are negative ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ULS Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic status one 0.697 0.495 0.135 0.109 - - evaluable two 0.920 0.850 0.074 0.043 - - evaluable RECOMMENDATION Model `two` has the most favorable descriptive combination of higher CFI/TLI and lower RMSEA/SRMR; interpret this recommendation together with theory, loadings, and residuals. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic covariance_only 0.677 0.569 0.187 0.143 - - with_means 0.677 0.569 0.187 0.131 - - status evaluable evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic one 0.677 0.569 0.187 0.143 7738.448 7805.176 three 0.931 0.896 0.092 0.065 7517.490 7595.339 status evaluable evaluable RECOMMENDATION Model `three` has the most favorable descriptive combination of higher CFI/TLI and lower RMSEA/SRMR; interpret this recommendation together with theory, loadings, and residuals. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic status only 0.856 0.760 0.187 0.114 - - evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic a 0.856 0.760 0.187 0.114 5143.372 5187.857 b 0.856 0.760 0.187 0.114 5143.372 5187.857 status evaluable evaluable RECOMMENDATION The best models tie on every available criterion; no positional recommendation is issued. CONCLUSION The best models tie on every available criterion; no positional recommendation is issued. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic status a - - - - - - not_evaluable b - - - - - - not_evaluable RECOMMENDATION At least two admissible, comparable models with finite fit indices are required. CONCLUSION At least two admissible, comparable models with finite fit indices are required. ANALYSIS ERRORS lavaan->lav_parse_formulas_open(): formula without valid operator at line 1, pos 1 not valid lavaan syntax ^ lavaan->lav_parse_formulas_open(): formula without valid operator at line 1, pos 1 also ??? invalid ^ The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` Testing metric invariance... The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` The default 'loading.method' has changed to "revised" in {EGAnet} version >= 2.0.7. For the previous default (version <= 2.0.6), use `loading.method = "original"` ================================================================================ PEARSON CORRELATIONS ================================================================================ Item item1 item2 item3 item1 1.000 0.833 -1.000 item2 0.833 1.000 -0.833 item3 -1.000 -0.833 1.000 RATIONALE User-specified method; automatic selection was not applied. REFERENCES Pearson, K. (1895). Note on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58, 240-242. https://doi.org/10.1098/rspl.1895.0041 Rhemtulla, M., Brosseau-Liard, P. E., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373. https://doi.org/10.1037/a0029315 ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 220 Items: 12 Complete: 220 Measurement: ordinal Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status reason Data sample All selected items Alpha (Cronbach) 0.912 Adequate >= 0.70 Data sample All selected items Ordinal alpha 0.924 Adequate >= 0.70 Data sample All selected items Omega 0.920 Adequate >= 0.70 ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Ordinal alpha if deleted i1 220 0.590 0.908 0.921 i2 220 0.581 0.908 0.921 i3 220 0.626 0.906 0.919 i4 220 0.575 0.909 0.921 i5 220 0.630 0.906 0.919 i6 220 0.645 0.905 0.918 i7 220 0.657 0.905 0.918 i8 220 0.729 0.901 0.915 i9 220 0.672 0.904 0.917 i10 220 0.677 0.904 0.917 i11 220 0.693 0.903 0.916 i12 220 0.719 0.902 0.915 Omega if deleted 0.916 0.915 0.914 0.917 0.914 0.913 0.913 0.909 0.912 0.912 0.910 0.906 COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Ordinal alpha applies the alpha formula to the polychoric matrix. Its estimand is the continuous latent-response scale, not the observed score. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155-167. https://doi.org/10.1007/s11336-008-9099-3 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6(1), 21-29. https://doi.org/10.22237/jmasm/1177992180 Number of categories should be increased in order to count frequencies. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 200 Items: 4 Complete: 200 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) 0.693 Inadequate Data sample All selected items Omega - not_evaluable reason < 0.70 inadmissible_model ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x1 200 0.713 0.449 0.468 x2 200 0.500 0.617 - x3 200 0.450 0.646 - x4 200 0.285 0.743 0.802 NON-EVALUABLE ITEM STATISTICS Item Index reason x2 omega_if_deleted inadmissible_model x3 omega_if_deleted inadmissible_model COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. WARNINGS lavaan->lav_object_post_check(): some estimated ov variances are negative REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 300 Items: 6 Complete: 300 Measurement: ordinal Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status reason Data sample All selected items Alpha (Cronbach) 0.848 Adequate >= 0.70 Data sample All selected items Ordinal alpha 0.868 Adequate >= 0.70 Data sample All selected items Omega 0.852 Adequate >= 0.70 ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Ordinal alpha if deleted i1 300 0.638 0.822 0.843 i2 300 0.600 0.829 0.851 i3 300 0.647 0.820 0.842 i4 300 0.653 0.819 0.841 i5 300 0.624 0.824 0.846 i6 300 0.619 0.825 0.848 Omega if deleted 0.825 0.832 0.825 0.822 0.824 0.826 COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Ordinal alpha applies the alpha formula to the polychoric matrix. Its estimand is the continuous latent-response scale, not the observed score. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155-167. https://doi.org/10.1007/s11336-008-9099-3 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6(1), 21-29. https://doi.org/10.22237/jmasm/1177992180 ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 10 Items: 1 Complete: 10 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) - not_evaluable Data sample All selected items Omega - not_evaluable reason insufficient_items insufficient_items ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x 10 - - - NON-EVALUABLE ITEM STATISTICS Item Index reason x item_rest insufficient_or_constant_scores x alpha_if_deleted insufficient_items x omega_if_deleted insufficient_items COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. CONCLUSION No requested reliability coefficient was evaluable. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 20 Items: 2 Complete: 20 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) - not_evaluable Data sample All selected items Spearman-Brown - not_evaluable Data sample All selected items Omega - not_evaluable reason zero_total_score_variance zero_denominator insufficient_items ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x 20 -1.000 - - y 20 -1.000 - - NON-EVALUABLE ITEM STATISTICS Item Index reason x alpha_if_deleted insufficient_items y alpha_if_deleted insufficient_items x omega_if_deleted insufficient_items y omega_if_deleted insufficient_items COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Spearman-Brown: 2*r/(1+r) for two items; the correlation type is retained in the results. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. CONCLUSION No requested reliability coefficient was evaluable. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 4 Items: 2 Complete: 4 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) - not_evaluable Data sample All selected items Omega - not_evaluable reason non_finite_input insufficient_items ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x 4 - - - y 4 - - - NON-EVALUABLE ITEM STATISTICS Item Index reason x item_rest insufficient_or_constant_scores y item_rest insufficient_or_constant_scores x alpha_if_deleted insufficient_items y alpha_if_deleted insufficient_items x omega_if_deleted insufficient_items y omega_if_deleted insufficient_items COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. CONCLUSION No requested reliability coefficient was evaluable. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 8 Items: 2 Complete: 8 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) - not_evaluable Data sample All selected items Spearman-Brown - not_evaluable Data sample All selected items Omega - not_evaluable reason zero_total_score_variance zero_denominator insufficient_items ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x 8 -1.000 - - y 8 -1.000 - - NON-EVALUABLE ITEM STATISTICS Item Index reason x alpha_if_deleted insufficient_items y alpha_if_deleted insufficient_items x omega_if_deleted insufficient_items y omega_if_deleted insufficient_items COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Spearman-Brown: 2*r/(1+r) for two items; the correlation type is retained in the results. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. CONCLUSION No requested reliability coefficient was evaluable. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 10 Items: 2 Complete: 10 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) -80.500 Inadequate Data sample All selected items Spearman-Brown -80.500 Inadequate Data sample All selected items Omega - not_evaluable reason < 0.70 < 0.70 insufficient_items ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x 10 -0.976 - - y 10 -0.976 - - NON-EVALUABLE ITEM STATISTICS Item Index reason x alpha_if_deleted insufficient_items y alpha_if_deleted insufficient_items x omega_if_deleted insufficient_items y omega_if_deleted insufficient_items COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Spearman-Brown: 2*r/(1+r) for two items; the correlation type is retained in the results. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 301 Items: 9 Complete: 301 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) 0.760 Adequate group1 visual Omega (supplied model) 0.612 Inadequate group1 textual Omega (supplied model) 0.885 Adequate group1 speed Omega (supplied model) 0.686 Inadequate reason >= 0.70 < 0.70 >= 0.70 < 0.70 AVERAGE VARIANCE EXTRACTED group factor coefficient estimate status reason group1 visual AVE 0.371 Inadequate < 0.50 group1 textual AVE 0.721 Adequate >= 0.50 group1 speed AVE 0.424 Inadequate < 0.50 ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x1 301 0.522 0.725 - x2 301 0.275 0.764 - x3 301 0.370 0.749 - x4 301 0.581 0.715 - x5 301 0.525 0.724 - x6 301 0.595 0.714 - x7 301 0.246 0.766 - x8 301 0.369 0.748 - x9 301 0.495 0.731 - NON-EVALUABLE ITEM STATISTICS Item Index reason x1 omega_if_deleted supplied_model_requires_explicit_refit x2 omega_if_deleted supplied_model_requires_explicit_refit x3 omega_if_deleted supplied_model_requires_explicit_refit x4 omega_if_deleted supplied_model_requires_explicit_refit x5 omega_if_deleted supplied_model_requires_explicit_refit x6 omega_if_deleted supplied_model_requires_explicit_refit x7 omega_if_deleted supplied_model_requires_explicit_refit x8 omega_if_deleted supplied_model_requires_explicit_refit x9 omega_if_deleted supplied_model_requires_explicit_refit COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Composite reliability: semTools::compRelSEM(model), per CFA factor and group, using its fitted sample and parameters. Defaults: obs.var=TRUE, tau.eq=FALSE, ord.scale=TRUE. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. AVE: semTools::AVE(model). Average variance extracted is not a reliability coefficient. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 3 Estimator: ML Model: Unidimensional Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Not evaluable: Package MVN is not installed. FIT INDICES Index Value Variant Evaluation Chi-square 0.000 base df 0 base p (chi-square) - base Chi-square/df - base CFI 1.000 base Adequate TLI 1.000 base Adequate RMSEA 0.000 base Adequate RMSEA lower CI 0.000 base RMSEA upper CI 0.000 base RMSEA p-close - base SRMR 0.000 base Adequate STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.621 0.067 <0.001 0.489 0.753 visual x2 0.479 0.063 <0.001 0.356 0.602 visual x3 0.710 0.071 <0.001 0.570 0.850 R2 Item R2 x1 0.386 x2 0.229 x3 0.504 REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 3 Estimator: ML Model: Unidimensional Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 39.341 301 <0.001 [Rejected] Kurtosis 0.385 301 0.700 [Not rejected] FIT INDICES Index Value Variant Evaluation Chi-square 0.000 base df 0 base p (chi-square) - base Chi-square/df - base CFI 1.000 base Adequate TLI 1.000 base Adequate RMSEA 0.000 base Adequate RMSEA lower CI 0.000 base RMSEA upper CI 0.000 base RMSEA p-close - base SRMR 0.000 base Adequate STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.621 0.067 <0.001 0.489 0.753 visual x2 0.479 0.063 <0.001 0.356 0.602 visual x3 0.710 0.071 <0.001 0.570 0.850 R2 Item R2 x1 0.386 x2 0.229 x3 0.504 RELIABILITY factor metric value status reason visual omega 0.800 Adequate >= 0.70 WARNINGS sentinel reliability warning REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 9 Estimator: MLR Model: Correlated factors Converged: TRUE RATIONALE Continuous items (20-129 cat.), normality test unavailable -> MLR as a precaution Reported corrected indices: scaled MARDIA MULTIVARIATE NORMALITY Not evaluable: Computation failed; inspect the analysis errors. FIT INDICES Index Value Variant Evaluation Chi-square (scaled) 87.132 scaled df 24 scaled p (chi-square) (scaled) <0.001 scaled Chi-square/df 3.630 scaled Acceptable CFI (scaled) 0.925 scaled Acceptable TLI (scaled) 0.888 scaled Poor RMSEA (scaled) 0.093 scaled Poor RMSEA lower CI (scaled) 0.073 scaled RMSEA upper CI (scaled) 0.115 scaled RMSEA p-close (scaled) <0.001 scaled SRMR 0.065 base Acceptable STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.772 0.074 <0.001 0.626 0.918 visual x2 0.424 0.068 <0.001 0.291 0.556 visual x3 0.581 0.066 <0.001 0.453 0.710 textual x4 0.852 0.025 <0.001 0.802 0.901 textual x5 0.855 0.021 <0.001 0.814 0.897 textual x6 0.838 0.023 <0.001 0.793 0.883 speed x7 0.570 0.070 <0.001 0.431 0.708 speed x8 0.723 0.079 <0.001 0.569 0.877 speed x9 0.665 0.088 <0.001 0.493 0.838 R2 Item R2 x1 0.596 x2 0.179 x3 0.338 x4 0.725 x5 0.731 x6 0.702 x7 0.324 x8 0.523 x9 0.442 FACTOR CORRELATIONS Factor1 Factor2 Correlation SE p Alert visual textual 0.459 0.073 <0.001 visual speed 0.471 0.119 <0.001 textual speed 0.283 0.085 <0.001 RELIABILITY factor metric value status reason visual omega 0.800 Adequate >= 0.70 SUGGESTIONS FOR REVIEW No Type Syntax MI EPC SameFactor 1 cross_loading visual =~ x9 36.411 0.577 FALSE 2 residual_covariance x7 ~~ x8 34.145 0.536 TRUE 3 cross_loading visual =~ x7 18.631 -0.422 FALSE 4 residual_covariance x8 ~~ x9 14.946 -0.423 TRUE NOTES 1. Consider only with substantive and methodologically defensible theory. 2. Same specific factor; inspect wording or method effects before freeing the covariance. 3. Consider only with substantive and methodologically defensible theory. 4. Same specific factor; inspect wording or method effects before freeing the covariance. ANALYSIS ERRORS sentinel diagnostic failure WARNINGS sentinel reliability warning REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399-419). Sage. Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507-514. https://doi.org/10.1007/BF02296192 Sorbom, D. (1989). Model modification. Psychometrika, 54(3), 371-384. https://doi.org/10.1007/BF02294623 Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 3 Estimator: ML Model: Unidimensional Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 39.341 301 <0.001 [Rejected] Kurtosis 0.385 301 0.700 [Not rejected] FIT INDICES Index Value Variant Evaluation Chi-square 0.000 base df 0 base p (chi-square) - base Chi-square/df - base CFI 1.000 base Adequate TLI 1.000 base Adequate RMSEA 0.000 base Adequate RMSEA lower CI 0.000 base RMSEA upper CI 0.000 base RMSEA p-close - base SRMR 0.000 base Adequate STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.621 0.067 <0.001 0.489 0.753 visual x2 0.479 0.063 <0.001 0.356 0.602 visual x3 0.710 0.071 <0.001 0.570 0.850 R2 Item R2 x1 0.386 x2 0.229 x3 0.504 ANALYSIS ERRORS sentinel reliability failure REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 10 Items: 2 Complete: 10 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) 1.000 Adequate Data sample All selected items Spearman-Brown 1.000 Adequate f Omega (supplied model) 0.800 Adequate reason >= 0.70 >= 0.70 >= 0.70 ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x 10 1.000 - - y 10 1.000 - - NON-EVALUABLE ITEM STATISTICS Item Index reason x alpha_if_deleted insufficient_items y alpha_if_deleted insufficient_items x omega_if_deleted supplied_model_requires_explicit_refit y omega_if_deleted supplied_model_requires_explicit_refit COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Spearman-Brown: 2*r/(1+r) for two items; the correlation type is retained in the results. Composite reliability: semTools::compRelSEM(model), per CFA factor and group, using its fitted sample and parameters. Defaults: obs.var=TRUE, tau.eq=FALSE, ord.scale=TRUE. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. WARNINGS sentinel semTools warning REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 3 Estimator: ML Model: Unidimensional Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 39.341 301 <0.001 [Rejected] Kurtosis 0.385 301 0.700 [Not rejected] FIT INDICES Index Value Variant Evaluation Chi-square 0.000 base df 0 base p (chi-square) - base Chi-square/df - base CFI 1.000 base Adequate TLI 1.000 base Adequate RMSEA 0.000 base Adequate RMSEA lower CI 0.000 base RMSEA upper CI 0.000 base RMSEA p-close - base SRMR 0.000 base Adequate STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.621 0.067 <0.001 0.489 0.753 visual x2 0.479 0.063 <0.001 0.356 0.602 visual x3 0.710 0.071 <0.001 0.570 0.850 R2 Item R2 x1 0.386 x2 0.229 x3 0.504 RELIABILITY factor metric value status reason visual Omega (composite reliability) 0.633 Inadequate < 0.70 visual Alpha (Cronbach) 0.626 Inadequate < 0.70 AVERAGE VARIANCE EXTRACTED factor metric value status reason visual AVE 0.369 Inadequate < 0.50 REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 9 Estimator: MLR Model: Correlated factors Converged: TRUE RATIONALE Estimator specified by the user Reported corrected indices: robust MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 344.905 301 <0.001 [Rejected] Kurtosis 2.830 301 0.005 [Rejected] FIT INDICES Index Value Variant Evaluation Chi-square (scaled) 87.132 scaled df 24 scaled p (chi-square) (scaled) <0.001 scaled Chi-square/df 3.630 scaled Acceptable CFI (robust) 0.930 robust Acceptable TLI (robust) 0.895 robust Poor RMSEA (robust) 0.092 robust Poor RMSEA lower CI (robust) 0.072 robust RMSEA upper CI (robust) 0.114 robust RMSEA p-close (robust) <0.001 robust SRMR 0.065 base Acceptable STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.772 0.074 <0.001 0.626 0.918 visual x2 0.424 0.068 <0.001 0.291 0.556 visual x3 0.581 0.066 <0.001 0.453 0.710 textual x4 0.852 0.025 <0.001 0.802 0.901 textual x5 0.855 0.021 <0.001 0.814 0.897 textual x6 0.838 0.023 <0.001 0.793 0.883 speed x7 0.570 0.070 <0.001 0.431 0.708 speed x8 0.723 0.079 <0.001 0.569 0.877 speed x9 0.665 0.088 <0.001 0.493 0.838 R2 Item R2 x1 0.596 x2 0.179 x3 0.338 x4 0.725 x5 0.731 x6 0.702 x7 0.324 x8 0.523 x9 0.442 FACTOR CORRELATIONS Factor1 Factor2 Correlation SE p Alert visual textual 0.459 0.073 <0.001 visual speed 0.471 0.119 <0.001 textual speed 0.283 0.085 <0.001 RELIABILITY factor metric value status reason visual Omega (composite reliability) 0.612 Inadequate < 0.70 textual Omega (composite reliability) 0.885 Adequate >= 0.70 speed Omega (composite reliability) 0.686 Inadequate < 0.70 visual Alpha (Cronbach) 0.626 Inadequate < 0.70 textual Alpha (Cronbach) 0.883 Adequate >= 0.70 speed Alpha (Cronbach) 0.688 Inadequate < 0.70 AVERAGE VARIANCE EXTRACTED factor metric value status reason visual AVE 0.371 Inadequate < 0.50 textual AVE 0.721 Adequate >= 0.50 speed AVE 0.424 Inadequate < 0.50 SUGGESTIONS FOR REVIEW No Type Syntax MI EPC SameFactor 1 cross_loading visual =~ x9 36.411 0.577 FALSE 2 residual_covariance x7 ~~ x8 34.145 0.536 TRUE 3 cross_loading visual =~ x7 18.631 -0.422 FALSE 4 residual_covariance x8 ~~ x9 14.946 -0.423 TRUE NOTES 1. Consider only with substantive and methodologically defensible theory. 2. Same specific factor; inspect wording or method effects before freeing the covariance. 3. Consider only with substantive and methodologically defensible theory. 4. Same specific factor; inspect wording or method effects before freeing the covariance. REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von Eye & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399-419). Sage. Satorra, A., & Bentler, P. M. (2001). A scaled difference chi-square test statistic for moment structure analysis. Psychometrika, 66(4), 507-514. https://doi.org/10.1007/BF02296192 Sorbom, D. (1989). Model modification. Psychometrika, 54(3), 371-384. https://doi.org/10.1007/BF02294623 Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 9 Estimator: ML Model: Second-order Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 344.905 301 <0.001 [Rejected] Kurtosis 2.830 301 0.005 [Rejected] FIT INDICES Index Value Variant Evaluation Chi-square 85.306 base df 24 base p (chi-square) <0.001 base Chi-square/df 3.554 base Acceptable CFI 0.931 base Acceptable TLI 0.896 base Poor RMSEA 0.092 base Poor RMSEA lower CI 0.071 base RMSEA upper CI 0.114 base RMSEA p-close <0.001 base SRMR 0.065 base Acceptable STANDARDIZED LOADINGS (95% CI) FactorLevel Factor Item Loading SE p Lower CI Upper CI L1 visual x1 0.772 0.055 <0.001 0.664 0.880 L1 visual x2 0.424 0.060 <0.001 0.307 0.540 L1 visual x3 0.581 0.055 <0.001 0.473 0.689 L1 textual x4 0.852 0.023 <0.001 0.807 0.896 L1 textual x5 0.855 0.022 <0.001 0.811 0.899 L1 textual x6 0.838 0.023 <0.001 0.792 0.884 L1 speed x7 0.570 0.053 <0.001 0.465 0.674 L1 speed x8 0.723 0.051 <0.001 0.624 0.822 L1 speed x9 0.665 0.051 <0.001 0.565 0.765 L2 g visual 0.873 0.115 <0.001 0.648 1.098 L2 g textual 0.525 0.079 <0.001 0.370 0.680 L2 g speed 0.539 0.085 <0.001 0.372 0.706 R2 Item R2 x1 0.596 x2 0.179 x3 0.338 x4 0.725 x5 0.731 x6 0.702 x7 0.324 x8 0.523 x9 0.442 visual 0.762 textual 0.276 speed 0.290 RELIABILITY FactorLevel factor metric value status reason L1 visual Omega (composite reliability) 0.467 Inadequate < 0.70 L1 textual Omega (composite reliability) 0.244 Inadequate < 0.70 L1 speed Omega (composite reliability) 0.199 Inadequate < 0.70 L1 visual Alpha (Cronbach) 0.626 Inadequate < 0.70 L1 textual Alpha (Cronbach) 0.883 Adequate >= 0.70 L1 speed Alpha (Cronbach) 0.688 Inadequate < 0.70 L2 g Omega (composite reliability) 0.552 Inadequate < 0.70 AVERAGE VARIANCE EXTRACTED FactorLevel factor metric value status reason L1 visual AVE 0.371 Inadequate < 0.50 L1 textual AVE 0.721 Adequate >= 0.50 L1 speed AVE 0.424 Inadequate < 0.50 L2 g AVE 0.202 Inadequate < 0.50 SUGGESTIONS FOR REVIEW No Type Syntax MI EPC SameFactor 1 cross_loading visual =~ x9 36.411 0.577 FALSE 2 residual_covariance x7 ~~ x8 34.145 0.536 TRUE 3 cross_loading g =~ x9 34.145 0.767 FALSE 4 cross_loading visual =~ x7 18.631 -0.422 FALSE 5 residual_covariance x8 ~~ x9 14.947 -0.423 TRUE 6 cross_loading g =~ x7 14.946 -0.517 FALSE NOTES 1. Consider only with substantive and methodologically defensible theory. 2. Same specific factor; inspect wording or method effects before freeing the covariance. 3. Consider only with substantive and methodologically defensible theory. 4. Consider only with substantive and methodologically defensible theory. 5. Same specific factor; inspect wording or method effects before freeing the covariance. 6. Consider only with substantive and methodologically defensible theory. REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In R. Cudeck, S. du Toit, & D. Sorbom (Eds.), Structural equation modeling: Present and future (pp. 195-216). Scientific Software International. Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Sorbom, D. (1989). Model modification. Psychometrika, 54(3), 371-384. https://doi.org/10.1007/BF02294623 Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 180 Items: 5 Complete: 180 Measurement: ordinal Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status reason Data sample All selected items Alpha (Cronbach) 0.779 Adequate >= 0.70 Data sample All selected items Ordinal alpha 0.804 Adequate >= 0.70 Data sample All selected items Omega 0.782 Adequate >= 0.70 ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Ordinal alpha if deleted i1 180 0.546 0.741 0.770 i2 180 0.558 0.737 0.765 i3 180 0.585 0.728 0.758 i4 180 0.596 0.724 0.751 i5 180 0.484 0.762 0.789 Omega if deleted 0.746 0.739 0.730 0.726 0.763 COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Ordinal alpha applies the alpha formula to the polychoric matrix. Its estimand is the continuous latent-response scale, not the observed score. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155-167. https://doi.org/10.1007/s11336-008-9099-3 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6(1), 21-29. https://doi.org/10.22237/jmasm/1177992180 ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 20 Items: 2 Complete: 20 Measurement: ordinal Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) - not_evaluable Data sample All selected items Ordinal alpha - not_evaluable Data sample All selected items Spearman-Brown - not_evaluable Data sample All selected items Omega - not_evaluable reason zero_total_score_variance polychoric_not_evaluable polychoric_not_evaluable insufficient_items ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Ordinal alpha if deleted i1 20 -1.000 - - i2 20 -1.000 - - Omega if deleted - - NON-EVALUABLE ITEM STATISTICS Item Index reason i1 alpha_if_deleted insufficient_items i2 alpha_if_deleted insufficient_items i1 alpha_ordinal_if_deleted insufficient_items i2 alpha_ordinal_if_deleted insufficient_items i1 omega_if_deleted insufficient_items i2 omega_if_deleted insufficient_items COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Ordinal alpha applies the alpha formula to the polychoric matrix. Its estimand is the continuous latent-response scale, not the observed score. Spearman-Brown: 2*r/(1+r) for two items; the correlation type is retained in the results. Omega: single-factor congeneric model (ML for continuous data; WLSMV for ordinal data), without equal-loading constraints. Ordinal omega targets observed-score reliability using Green and Yang's correction. It does not establish unidimensionality or good model fit. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. CONCLUSION No requested reliability coefficient was evaluable. ANALYSIS ERRORS sentinel polychoric failure REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155-167. https://doi.org/10.1007/s11336-008-9099-3 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6(1), 21-29. https://doi.org/10.22237/jmasm/1177992180 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 500 Items: 3 Estimator: ML Model: Unidimensional Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 0.072 500 1.000 [Not rejected] Kurtosis 1.342 500 0.180 [Not rejected] FIT INDICES Index Value Variant Evaluation Chi-square 0.000 base df 0 base p (chi-square) - base Chi-square/df - base Not evaluable CFI 1.000 base Not evaluable TLI 1.000 base Not evaluable RMSEA 0.000 base Not evaluable RMSEA lower CI 0.000 base RMSEA upper CI 0.000 base RMSEA p-close - base SRMR 0.000 base Not evaluable STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI f x1 1.131 0.023 <0.001 1.087 1.176 f x2 0.707 0.025 <0.001 0.657 0.757 f x3 0.707 0.025 <0.001 0.657 0.757 R2 Item R2 x1 - x2 0.500 x3 0.500 CONCLUSION The CFA solution is inadmissible: post_check_failed, negative_variance, heywood_loading. WARNINGS lavaan->lav_object_post_check(): some estimated ov variances are negative The model converged, but the solution is inadmissible (post_check_failed, negative_variance, heywood_loading). Fit interpretation and reliability are not evaluable. Heywood case(s) detected - negative variance in: x1 Factor loading(s) > 1.0 detected: x1 REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 3 Estimator: ML Model: Unidimensional Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 39.341 301 <0.001 [Rejected] Kurtosis 0.385 301 0.700 [Not rejected] FIT INDICES Index Value Variant Evaluation Chi-square 0.000 base df 0 base p (chi-square) - base Chi-square/df - base CFI 1.000 base Adequate TLI 1.000 base Adequate RMSEA 0.000 base Adequate RMSEA lower CI 0.000 base RMSEA upper CI 0.000 base RMSEA p-close - base SRMR 0.000 base Adequate STANDARDIZED LOADINGS (95% CI) Factor Item Loading SE p Lower CI Upper CI visual x1 0.621 0.067 <0.001 0.489 0.753 visual x2 0.479 0.063 <0.001 0.356 0.602 visual x3 0.710 0.071 <0.001 0.570 0.850 R2 Item R2 x1 0.386 x2 0.229 x3 0.504 RELIABILITY factor metric value status reason visual Omega (composite reliability) 0.633 Inadequate < 0.70 visual Alpha (Cronbach) 0.626 Inadequate < 0.70 AVERAGE VARIANCE EXTRACTED factor metric value status reason visual AVE 0.369 Inadequate < 0.50 REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ CONFIRMATORY FACTOR ANALYSIS ================================================================================ DATA AND METHOD N: 301 Items: 9 Estimator: ML Model: Second-order Converged: TRUE RATIONALE Estimator specified by the user Uncorrected indices reported (classical ML estimator) MARDIA MULTIVARIATE NORMALITY Test Statistic N p Decision Skewness 344.905 301 <0.001 [Rejected] Kurtosis 2.830 301 0.005 [Rejected] FIT INDICES Index Value Variant Evaluation Chi-square 85.306 base df 24 base p (chi-square) <0.001 base Chi-square/df 3.554 base Acceptable CFI 0.931 base Acceptable TLI 0.896 base Poor RMSEA 0.092 base Poor RMSEA lower CI 0.071 base RMSEA upper CI 0.114 base RMSEA p-close <0.001 base SRMR 0.065 base Acceptable STANDARDIZED LOADINGS (95% CI) FactorLevel Factor Item Loading SE p Lower CI Upper CI L1 visual x1 0.772 0.055 <0.001 0.664 0.880 L1 visual x2 0.424 0.060 <0.001 0.307 0.540 L1 visual x3 0.581 0.055 <0.001 0.473 0.689 L1 textual x4 0.852 0.023 <0.001 0.807 0.896 L1 textual x5 0.855 0.022 <0.001 0.811 0.899 L1 textual x6 0.838 0.023 <0.001 0.792 0.884 L1 speed x7 0.570 0.053 <0.001 0.465 0.674 L1 speed x8 0.723 0.051 <0.001 0.624 0.822 L1 speed x9 0.665 0.051 <0.001 0.565 0.765 L2 g visual 0.873 0.115 <0.001 0.648 1.098 L2 g textual 0.525 0.079 <0.001 0.370 0.680 L2 g speed 0.539 0.085 <0.001 0.372 0.706 R2 Item R2 x1 0.596 x2 0.179 x3 0.338 x4 0.725 x5 0.731 x6 0.702 x7 0.324 x8 0.523 x9 0.442 visual 0.762 textual 0.276 speed 0.290 RELIABILITY FactorLevel factor metric value status reason L1 visual Omega (composite reliability) 0.467 Inadequate < 0.70 L1 textual Omega (composite reliability) 0.244 Inadequate < 0.70 L1 speed Omega (composite reliability) 0.199 Inadequate < 0.70 L1 visual Alpha (Cronbach) 0.626 Inadequate < 0.70 L1 textual Alpha (Cronbach) 0.883 Adequate >= 0.70 L1 speed Alpha (Cronbach) 0.688 Inadequate < 0.70 L2 g Omega (composite reliability) 0.552 Inadequate < 0.70 AVERAGE VARIANCE EXTRACTED FactorLevel factor metric value status reason L1 visual AVE 0.371 Inadequate < 0.50 L1 textual AVE 0.721 Adequate >= 0.50 L1 speed AVE 0.424 Inadequate < 0.50 L2 g AVE 0.202 Inadequate < 0.50 SUGGESTIONS FOR REVIEW No Type Syntax MI EPC SameFactor 1 cross_loading visual =~ x9 36.411 0.577 FALSE 2 residual_covariance x7 ~~ x8 34.145 0.536 TRUE 3 cross_loading g =~ x9 34.145 0.767 FALSE 4 cross_loading visual =~ x7 18.631 -0.422 FALSE 5 residual_covariance x8 ~~ x9 14.947 -0.423 TRUE 6 cross_loading g =~ x7 14.946 -0.517 FALSE NOTES 1. Consider only with substantive and methodologically defensible theory. 2. Same specific factor; inspect wording or method effects before freeing the covariance. 3. Consider only with substantive and methodologically defensible theory. 4. Consider only with substantive and methodologically defensible theory. 5. Same specific factor; inspect wording or method effects before freeing the covariance. 6. Consider only with substantive and methodologically defensible theory. REFERENCES Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555 Hancock, G. R., & Mueller, R. O. (2001). Rethinking construct reliability within latent variable systems. In R. Cudeck, S. du Toit, & D. Sorbom (Eds.), Structural equation modeling: Present and future (pp. 195-216). Scientific Software International. Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press. Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.2307/2334770 McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Sorbom, D. (1989). Model modification. Psychometrika, 54(3), 371-384. https://doi.org/10.1007/BF02294623 Viladrich, C., Angulo-Brunet, A., & Doval, E. (2017). A journey around alpha and omega to estimate internal consistency reliability. Anales de Psicologia, 33(3), 755-782. https://doi.org/10.6018/analesps.33.3.268401 ================================================================================ RELIABILITY ================================================================================ DATA AND METHOD N: 301 Items: 9 Complete: 301 Measurement: continuous Keying: none RELIABILITY COEFFICIENTS group factor coefficient estimate status Data sample All selected items Alpha (Cronbach) 0.760 Adequate Pasteur visual Omega (supplied model) 0.584 Inadequate Grant-White visual Omega (supplied model) 0.661 Inadequate Pasteur textual Omega (supplied model) 0.877 Adequate Grant-White textual Omega (supplied model) 0.878 Adequate Pasteur speed Omega (supplied model) 0.620 Inadequate Grant-White speed Omega (supplied model) 0.766 Adequate reason >= 0.70 < 0.70 < 0.70 >= 0.70 >= 0.70 < 0.70 >= 0.70 AVERAGE VARIANCE EXTRACTED group factor coefficient estimate status reason Pasteur visual AVE 0.382 Inadequate < 0.50 Grant-White visual AVE 0.400 Inadequate < 0.50 Pasteur textual AVE 0.707 Adequate >= 0.50 Grant-White textual AVE 0.706 Adequate >= 0.50 Pasteur speed AVE 0.351 Inadequate < 0.50 Grant-White speed AVE 0.521 Adequate >= 0.50 ITEM ANALYSIS: RELIABILITY IF DELETED item N cases Item-rest r Alpha if deleted Omega if deleted x1 301 0.522 0.725 - x2 301 0.275 0.764 - x3 301 0.370 0.749 - x4 301 0.581 0.715 - x5 301 0.525 0.724 - x6 301 0.595 0.714 - x7 301 0.246 0.766 - x8 301 0.369 0.748 - x9 301 0.495 0.731 - NON-EVALUABLE ITEM STATISTICS Item Index reason x1 omega_if_deleted supplied_model_requires_explicit_refit x2 omega_if_deleted supplied_model_requires_explicit_refit x3 omega_if_deleted supplied_model_requires_explicit_refit x4 omega_if_deleted supplied_model_requires_explicit_refit x5 omega_if_deleted supplied_model_requires_explicit_refit x6 omega_if_deleted supplied_model_requires_explicit_refit x7 omega_if_deleted supplied_model_requires_explicit_refit x8 omega_if_deleted supplied_model_requires_explicit_refit x9 omega_if_deleted supplied_model_requires_explicit_refit COMPUTATION AND INTERPRETATION Alpha (Cronbach): k/(k-1) * (1 - sum of item variances / variance of the sum). Uses the raw covariance matrix with pairwise available observations. Composite reliability: semTools::compRelSEM(model), per CFA factor and group, using its fitted sample and parameters. Defaults: obs.var=TRUE, tau.eq=FALSE, ord.scale=TRUE. Corrected item-total correlation excludes the item from the sum and uses full-scale complete cases. Alpha uses pairwise observations; omega uses complete cases per fit. Item deletion refits omega and may change N. A coefficient increase alone does not justify deleting an item. AVE: semTools::AVE(model). Average variance extracted is not a reliability coefficient. Selected-item alpha and model factor coefficients may refer to different scores. Overall alpha does not establish unidimensionality. REFERENCES Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555 Jorgensen, T. D., Pornprasertmanit, S., Schoemann, A. M., & Rosseel, Y. (2026). semTools: Useful tools for structural equation modeling (Version 0.5.10) [R package]. https://CRAN.R-project.org/package=semTools McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates. Reporte guardado: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609f1e26612e/psychomatic_report_20261023_181417_1609f69b62278.xlsx Report saved: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609f1e26612e/psychomatic_report_20261023_181417_1609f6401070d.xlsx Report saved: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609f3b43f3d0/psychomatic_report_20261023_181418_1609f7d3dc289.xlsx; /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609f3b43f3d0/psychomatic_report_20261023_181418_1609f7d3dc289.docx Report saved: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609f6d19fa5f/psychomatic_report_20261023_181418_1609f4484aaee.xlsx Report saved: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609f6d19fa5f/psychomatic_report_20261023_181419_1609f5b349e23.xlsx Report saved: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609faadfe99/explicit destination/descriptives.xlsx Report saved: /private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/proyecto reportes-á-1609faadfe99/explicit destination/descriptives.xlsx ================================================================================ ITEM SCREENING ================================================================================ DESCRIPTIVES Item N Missing Missing (%) Mean SD Min Max i1 6 0.000 0.000 3.167 1.472 1.000 5.000 i2 6 0.000 0.000 3.167 1.169 2.000 5.000 i3 6 0.000 0.000 2.833 1.472 1.000 5.000 DISTRIBUTION AND ENDPOINTS Item Skewness Kurtosis Categories Floor (%) Ceiling (%) i1 -0.232 -1.716 5.000 16.700 16.700 i2 0.371 -1.618 4.000 33.300 16.700 i3 0.232 -1.716 5.000 16.700 16.700 ITEM CHECKS AND FLAGS Item Item-rest r No variance Floor Ceiling Review key i1 0.976 No No No No i2 0.786 No No No No i3 0.754 No No No No ================================================================================ ALIGNMENT ================================================================================ SUMMARY Parameter R2 Noninvariant (%) Cutoff (%) Compatible Loadings 1.000 0.000 25.000 TRUE Intercepts 0.953 0.000 25.000 TRUE LOADINGS Item Joint estimate Flagged N Noninvariant (%) item1 0.715 0.000 0.000 item2 0.796 0.000 0.000 item3 0.750 0.000 0.000 INTERCEPTS Item Joint estimate Flagged N Noninvariant (%) item1 0.011 0.000 0.000 item2 -0.017 0.000 0.000 item3 -0.000 0.000 0.000 GROUP PARAMETERS Group Latent mean Latent SD G1 0.000 1.000 G2 0.107 0.985 CONCLUSION Conclusion: the scale meets the percentage-based alignment invariance criterion. WARNINGS the standard deviation is zero REFERENCES 1. Asparouhov, T., & Muthen, B. (2014). Multiple-group factor analysis alignment. Structural Equation Modeling: A Multidisciplinary Journal, 21(4), 495-508. https://doi.org/10.1080/10705511.2014.919210 2. Marsh, H. W., Guo, J., Parker, P. D., Nagengast, B., Asparouhov, T., Muthen, B., & Dicke, T. (2018). What to do when scalar invariance fails: The extended alignment method for multi-group factor analysis comparison of latent means across many groups. Psychological Methods, 23(3), 524-545. https://doi.org/10.1037/met0000113 3. Robitzsch, A., & Ludtke, O. (2023). Why full, partial, or approximate measurement invariance are not a prerequisite for meaningful and valid group comparisons. Structural Equation Modeling: A Multidisciplinary Journal, 30(6), 859-870. https://doi.org/10.1080/10705511.2023.2191292 4. Fischer, R., & Karl, J. A. (2019). A primer to (cross-cultural) multi-group invariance testing possibilities in R. Frontiers in Psychology, 10, Article 1507. https://doi.org/10.3389/fpsyg.2019.01507 5. Muthen, B., & Asparouhov, T. (2014). IRT studies of many groups: The alignment method. Frontiers in Psychology, 5, Article 978. https://doi.org/10.3389/fpsyg.2014.00978 Saving _problems/test-reporting-audit-378.R Saving _problems/test-reporting-regressions-127.R ================================================================================ PEARSON CORRELATIONS ================================================================================ Item a b c a 1.000 1.000 - b 1.000 1.000 - c - - 1.000 RATIONALE User-specified method; automatic selection was not applied. REFERENCES Pearson, K. (1895). Note on regression and inheritance in the case of two parents. Proceedings of the Royal Society of London, 58, 240-242. https://doi.org/10.1098/rspl.1895.0041 Rhemtulla, M., Brosseau-Liard, P. E., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373. https://doi.org/10.1037/a0029315 ================================================================================ DESCRIPTIVES ================================================================================ N Missing Mean SD Min Max Skewness Kurtosis 5000 0.0 2500.5 1443.5 0.8 4999.9 0.0 -1.2 5000 0.0 2500.5 1443.5 0.2 5000.7 -0.0 -1.2 5000 0.0 2500.5 1443.5 1.1 5001.4 0.0 -1.2 5000 0.0 2500.5 1443.5 0.8 5000.2 -0.0 -1.2 5000 0.0 2500.5 1443.5 -0.2 5001.0 0.0 -1.2 5000 0.0 2500.5 1443.5 2.0 4999.8 0.0 -1.2 5000 0.0 2500.5 1443.5 2.0 5000.1 0.0 -1.2 5000 0.0 2500.5 1443.6 1.2 5000.0 0.0 -1.2 5000 0.0 2500.5 1443.5 0.5 5000.3 -0.0 -1.2 5000 0.0 2500.5 1443.5 -0.1 4999.9 0.0 -1.2 5000 0.0 2500.5 1443.5 0.6 5000.1 0.0 -1.2 5000 0.0 2500.5 1443.5 1.0 4999.5 0.0 -1.2 5000 0.0 2500.5 1443.5 0.9 4998.8 0.0 -1.2 5000 0.0 2500.5 1443.5 0.2 5000.3 -0.0 -1.2 5000 0.0 2500.5 1443.5 1.8 5000.0 -0.0 -1.2 5000 0.0 2500.5 1443.6 1.0 5000.4 -0.0 -1.2 5000 0.0 2500.5 1443.5 1.6 4999.2 0.0 -1.2 5000 0.0 2500.5 1443.5 -0.6 5000.1 -0.0 -1.2 5000 0.0 2500.5 1443.5 1.0 4999.4 -0.0 -1.2 5000 0.0 2500.5 1443.5 -1.1 5000.1 -0.0 -1.2 1. Item: c.0.842626662776525..0.801142489849665..2.11079509542715..5.00906070468364.. 2. Item: c.0.195521289570962..3.90513967302929..1.43319629693866..3.7749525773554.. 3. Item: c.1.11212957750539..3.65974295845077..2.33278038157746..4.31642560183883.. 4. Item: c.0.849955382709193..2.84242909884767..2.04247810872218..2.43271066659511.. 5. Item: c..0.204569212267099..2.0706547586808..4.90420402227764..3.52905463788173.. 6. Item: c.1.97150505971805..2.13344643925731..4.48255394003184..4.83121416850377.. 7. Item: c.2.02685110010269..2.38703711750417..3.22612556590309..4.0761256161014.. 8. Item: c.1.75373906744058..1.19512048496315..1.45328365607513..4.10048689383849.. 9. Item: c.0.471054539255708..2.03647139339198..2.23847696605452..2.30033450977686.. 10. Item: c..0.133822085315511..2.40715629511466..4.17322476146407..4.39242886244913.. 11. Item: c.0.606830236176887..0.712221457848565..2.55511828693393..4.64683785819442.. 12. Item: c.0.974815440192161..2.9027235399088..3.58341644537995..5.51658656498918.. 13. Item: c.2.09757679295376..1.46010651741052..0.921263038279151..5.66269945409347.. 14. Item: c.0.161339814224922..1.15880393311958..2.81970643174861..4.30500478202209.. 15. Item: c.1.83365533462426..2.09865412075866..3.12440523311859..4.09649573723694.. 16. Item: c.1.01582852005613..2.1062623091648..3.27663307103526..6.3579760121667.. 17. Item: c.1.92695400714134..1.61812985813226..4.44292214469943..4.14074802586767.. 18. Item: c..0.612749247342117..3.71118698136721..2.85016067795438..3.3018693998454.. 19. Item: c.1.03285325252601..3.07264679683736..3.46768088616751..4.24109782576982.. 20. Item: c..1.14684525583256..3.30078109318079..2.40926617377371..4.52362751811694.. ================================================================================ DESCRIPTIVES ================================================================================ Item N Missing Mean SD Min Max Skewness Kurtosis q 3 0.0 0.3 0.6 0.0 1.0 0.4 - RESPONSE PERCENTAGES item category n percent q 0 2 66.7 q 1 1 33.3 ================================================================================ DESCRIPTIVES ================================================================================ Item N Missing Mean SD Min Max Skewness Kurtosis q 7 1.000 2.143 0.900 1.000 3.000 -0.216 -1.903 z 8 0.000 0.450 0.245 0.100 0.800 0.000 -1.651 RESPONSE PERCENTAGES item category n percent q 1 2 28.571 q 2 2 28.571 q 3 3 42.857 Saving _problems/test-scoring-correlations-245.R ================================================================================ ITEM SCREENING ================================================================================ DESCRIPTIVES Item N Missing Missing (%) Mean SD Min Max item1 5 1.000 16.700 3.000 1.581 1.000 5.000 item2 6 0.000 0.000 2.667 1.633 1.000 5.000 item3 6 0.000 0.000 1.000 0.000 1.000 1.000 DISTRIBUTION AND ENDPOINTS Item Skewness Kurtosis Categories Floor (%) Ceiling (%) item1 0.000 -1.912 5.000 20.000 20.000 item2 0.213 -1.865 5.000 33.300 16.700 item3 - - 1.000 100.000 100.000 ITEM CHECKS AND FLAGS Item Item-rest r No variance Floor Ceiling Review key item1 -1.000 No No No Yes item2 -1.000 No No No Yes item3 - Yes Yes Yes No ================================================================================ ITEM SCREENING ================================================================================ DESCRIPTIVES Item N Missing Missing (%) Mean SD Min Max item1 5 0.000 0.000 3.000 1.581 1.000 5.000 item2 5 0.000 0.000 3.800 1.304 2.000 5.000 item3 5 0.000 0.000 2.800 1.643 1.000 5.000 DISTRIBUTION AND ENDPOINTS Item Skewness Kurtosis Categories Floor (%) Ceiling (%) item1 0.000 -1.912 5.000 20.000 20.000 item2 -0.260 -1.958 4.000 20.000 40.000 item3 0.249 -1.990 4.000 20.000 20.000 ITEM CHECKS AND FLAGS Item Item-rest r No variance Floor Ceiling Review key item1 0.988 No No No No item2 0.949 No No No No item3 0.946 No No No No ================================================================================ DIFFERENTIAL ITEM FUNCTIONING ================================================================================ SUMMARY n_items flagged_items uniform_flags nonuniform_flags not_evaluable_items 3 1.000 1.000 0.000 0.000 flagged_pct alpha groups 0.333 0.050 A, B recommendation: Several items show possible DIF; confirm with a dedicated DIF analysis before final decisions. ITEM RESULTS item p_uniform p_nonuniform effect_size status reason item1 0.798 0.130 0.033 evaluable - item2 0.008 0.089 0.105 evaluable - item3 0.918 0.746 0.002 evaluable - INTERPRETATION item dif_type severity item1 none no_flag item2 uniform review item3 none no_flag 1. decision: No statistical DIF evidence in this screening. 1. recommendation: Retain unless theory or substantive evidence suggests review. 2. decision: Possible uniform DIF. 2. recommendation: Review item content and systematic group differences. 3. decision: No statistical DIF evidence in this screening. 3. recommendation: Retain unless theory or substantive evidence suggests review. REFERENCES Choi, S. W., Gibbons, L. E., & Crane, P. K. (2011). lordif: An R package for detecting differential item functioning using iterative hybrid ordinal logistic regression/item response theory and Monte Carlo simulations. Journal of Statistical Software, 39(8), 1-30. https://doi.org/10.18637/jss.v039.i08 Jodoin, M. G., & Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with the logistic regression procedure for DIF detection. Applied Measurement in Education, 14(4), 329-349. https://doi.org/10.1207/S15324818AME1404_2 Mellenbergh, G. J. (1982). Contingency table models for assessing item bias. Journal of Educational Statistics, 7(2), 105-118. https://doi.org/10.3102/10769986007002105 Steinberg, L., & Thissen, D. (2006). Using effect sizes for research reporting: Examples using item response theory to analyze differential item functioning. Psychological Methods, 11(4), 402-415. https://doi.org/10.1037/1082-989X.11.4.402 Swaminathan, H., & Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27(4), 361-370. https://doi.org/10.1111/j.1745-3984.1990.tb00754.x ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 301 Estimator: ML Selection: User RATIONALE Estimator specified by the user FIT model CFI (base) TLI (base) RMSEA (base) SRMR (base) aic bic one_factor 0.677 0.569 0.187 0.143 7738.448 7805.176 three_factor 0.931 0.896 0.092 0.065 7517.490 7595.339 status evaluable evaluable RECOMMENDATION Model `three_factor` has the most favorable descriptive combination of higher CFI/TLI and lower RMSEA/SRMR; interpret this recommendation together with theory, loadings, and residuals. ================================================================================ MODEL COMPARISON ================================================================================ DATA AND METHOD N: 100 Estimator: WLSMV Selection: User RATIONALE Estimator specified by the user FIT model CFI (scaled) TLI (scaled) RMSEA (scaled) SRMR (base) aic bic one_factor 1.000 1.003 0.000 0.012 - - two_factor 1.000 1.003 0.000 0.012 - - status evaluable evaluable RECOMMENDATION Model `one_factor` has the most favorable descriptive combination of higher CFI/TLI and lower RMSEA/SRMR; interpret this recommendation together with theory, loadings, and residuals. ================================================================================ ITEM RESPONSE THEORY ================================================================================ MODEL SUMMARY model itemtype n n_items items_to_review mean_discrimination grm graded 80 4 0.000 3.547 recommendation: No major item flags; review item content and test information before concluding. ITEM PARAMETERS item a1 d1 d2 d3 d4 discrimination_magnitude a b1 ord1 3.997 3.393 0.292 -1.139 -3.198 3.997 3.997 -0.849 ord2 3.433 3.785 0.926 -0.349 -3.296 3.433 3.433 -1.103 ord3 3.190 2.428 0.728 -1.053 -3.102 3.190 3.190 -0.761 ord4 3.568 3.185 1.026 -0.105 -2.891 3.568 3.568 -0.893 b2 b3 b4 -0.073 0.285 0.800 -0.270 0.102 0.960 -0.228 0.330 0.972 -0.288 0.029 0.810 INTERPRETATION item discrimination discrimination_level difficulty_center threshold_min ord1 3.997 Very high 0.041 -0.849 ord2 3.433 Very high -0.078 -1.103 ord3 3.190 Very high 0.078 -0.761 ord4 3.568 Very high -0.085 -0.893 threshold_max threshold_ordered 0.800 TRUE 0.960 TRUE 0.972 TRUE 0.810 TRUE 1. recommendation: No major flag; review together with item content and test information. 2. recommendation: No major flag; review together with item content and test information. 3. recommendation: No major flag; review together with item content and test information. 4. recommendation: No major flag; review together with item content and test information. ANALYSIS ERRORS Statistic cannot be calculated (too few degrees of freedom) REFERENCES Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573. https://doi.org/10.1007/BF02293814 Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37(1), 29-51. https://doi.org/10.1007/BF02291411 Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459. https://doi.org/10.1007/BF02293801 Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. https://doi.org/10.18637/jss.v048.i06 Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176. https://doi.org/10.1177/014662169201600206 [ FAIL 4 | WARN 0 | SKIP 13 | PASS 3398 ] ══ Skipped tests (13) ══════════════════════════════════════════════════════════ • Extended regression: set PSYCHOMATIC_EXTENDED_TESTS=true (13): 'test-console-workflow.R:102:3', 'test-console-workflow.R:118:3', 'test-esem-failures.R:2:3', 'test-esem-native.R:7:7', 'test-esem-native.R:7:7', 'test-esem-native.R:7:7', 'test-esem-native.R:7:7', 'test-esem-reporting.R:27:3', 'test-invariance-partial-native.R:2:3', 'test-minimal-reliability.R:67:3', 'test-network-integration.R:10:3', 'test-network-integration.R:66:3', 'test-network-integration.R:88:3' ══ Failed tests ════════════════════════════════════════════════════════════════ ── Failure ('test-invariance-partial.R:911:3'): language precedence, methods, and reports preserve raw results ── Expected `out$report_path` to be identical to `normalizePath(path, winslash = "/")`. Differences: actual vs expected - "/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/partial-invariance-1609f51f68789.xlsx" + "/private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/partial-invariance-1609f51f68789.xlsx" ── Failure ('test-reporting-audit.R:378:3'): psychomatic_report validates inputs and preflights all outputs atomically ── Expected `as.character(visible$value)` to be identical to `normalizePath(excel, winslash = "/")`. Differences: actual vs expected - "/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/psychomatic-report-1609f65897385.xlsx" + "/private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/psychomatic-report-1609f65897385.xlsx" ── Failure ('test-reporting-regressions.R:127:3'): export_cfa uses the common mapped writer and returns paths ── Expected `as.character(visible$value)` to be identical to `normalizePath(path, winslash = "/")`. Differences: actual vs expected - "/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/psychomatic-cfa-common-1609f594dad1.xlsx" + "/private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/psychomatic-cfa-common-1609f594dad1.xlsx" ── Failure ('test-scoring-correlations.R:242:3'): safe paths add only the requested extension and never overwrite by default ── Expected `PsychoMatic:::.pm_safe_output_path(...)` to be identical to `xlsx`. Differences: actual vs expected - "/private/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T/RtmpeHmTwA/working_dir/RtmpBnFxFT/file1609f781e9a40.xlsx" + "/var/folders/pk/n4bndnt1287ctrd_ftthnnnr0000gp/T//RtmpeHmTwA/working_dir/RtmpBnFxFT/file1609f781e9a40.xlsx" [ FAIL 4 | WARN 0 | SKIP 13 | PASS 3398 ] Error: ! Test failures. Execution halted * checking for unstated dependencies in vignettes ... OK * checking package vignettes ... OK * checking re-building of vignette outputs ... [15s/17s] OK * checking PDF version of manual ... OK * checking HTML version of manual ... OK * checking for detritus in the temp directory ... OK * DONE Status: 1 ERROR See ‘/Users/ripley/R/packages/tests-devel/PsychoMatic.Rcheck/00check.log’ for details. 221.62 real 193.53 user 24.52 sys