| 1. Introduction | |
| Multilevel analysis | |
| Probability models | |
| This book | |
| Prerequisites | |
| Notation | |
| 2. Multilevel Theories, Multi-Stage Sampling and Multilevel Models | |
| Dependence as a nuisance | |
| Dependence as an interesting phenomenon | |
| Macro-level, micro-level, and cross-level relations | |
| Glommary | |
| 3. Statistical Treatment of Clustered Data | |
| Aggregation | |
| Disaggregation | |
| The intraclass correlation | |
| Within-group and between group variance | |
| Testing for group differences | |
| Design effects in two-stage samples | |
| Reliability of aggregated variables | |
| Within-and between group relations | |
| Regressions | |
| Correlations | |
| Estimation of within-and between-group correlations | |
| Combination of within-group evidence | |
| Glommary | |
| 4. The Random Intercept Model | |
| Terminology and notation | |
| A regression model: fixed effects only | |
| Variable intercepts: fixed or random parameters? | |
| When to use random coefficient models | |
| Definition of the random intercept model | |
| More explanatory variables | |
| Within-and between-group regressions | |
| Parameter estimation | |
| 'Estimating' random group effects: posterior means | |
| Posterior confidence intervals | |
| Three-level random intercept models | |
| Glommary | |
| 5. The Hierarchical Linear Model | |
| Random slopes | |
| Heteroscedasticity | |
| Do not force ?01 to be 0! | |
| Interpretation of random slope variances | |
| Explanation of random intercepts and slopes | |
| Cross-level interaction effects | |
| A general formulation of fixed and random parts | |
| Specification of random slope models | |
| Centering variables with random slopes? | |
| Estimation | |
| Three or more levels | |
| Glommary | |
| 5. Testing and Model Specification | |
| Tests for fixed parameters | |
| Multiparameter tests for fixed effects | |
| Deviance tests | |
| More powerful tests for variance parameters | |
| Other tests for parameters in the random part | |
| Confidence intervals for parameters in the random part | |
| Model specification | |
| Working upward from level one | |
| Joint consideration of level-one and level-two variables | |
| Concluding remarks on model specification | |
| Glommary | |
| 7. How Much Does the Model Explain? | |
| Explained variance | |
| Negative values of R2? | |
| Definition of the proportion of explained variance in two-level models | |
| Explained variance in three-level models | |
| Explained variance in models with random slopes | |
| Components of variance | |
| Random intercept models | |
| Random slope models | |
| Glommary | |
| 8. Heteroscedasticity | |
| Heteroscedasticity at level one | |
| Linear variance functions | |
| Quadratic variance functions | |
| Heteroscedasticity at level two | |
| Glommary | |
| 9. Missing Data | |
| General issues for missing data | |
| Implications for design | |
| Missing values of the dependent variable | |
| Full maximum likelihood | |
| Imputation | |
| The imputation method | |
| Putting together the multiple results | |
| Multiple imputations by chained equations | |
| Choice of the imputation model | |
| Glommary | |
| 10. Assumptions of the Hierarchical Linear Model | |
| Assumptions of the hierarchical linear model | |
| Following the logic of the hierarchical linear model | |
| Include contextual effects | |
| Check whether variables have random effects | |
| Explained variance | |
| Specification of the fixed part | |
| Specification of the random part | |
| Testing for heteroscedasticity | |
| What to do in case of heteroscedasticity | |
| Inspection of level-one residuals | |
| Residuals at level two | |
| Influence of level-two units | |
| More general distributional assumptions | |
| Glommary | |
| 11. Designing Multilevel Studies | |
| Some introductory notes on power | |
| Estimating a population mean | |
| Measurement of subjects | |
| Estimating association between variables | |
| Cross-level interaction effects | |
| Allocating treatment to groups or individuals | |
| Exploring the variance structure | |
| The intraclass correlation | |
| Variance parameters | |
| Glommary | |
| 12. Other Methods and Models | |
| Bayesian inference | |
| Sandwich estimators for standard errors | |
| Latent class models | |
| Glommary | |
| 13. Imperfect Hierarchies | |
| A two-level model with a crossed random factor | |
| Crossed random effects in three-level models | |
| Multiple membership models | |
| Multiple membership multiple classification models | |
| Glommary | |
| 14. Survey Weights | |
| Model-based and design-based inference | |
| Descriptive and analytic use of surveys | |
| Two kinds of weights | |
| Choosing between model-based and design-based analysis | |
| Inclusion probabilities and two-level weights | |
| Exploring the informativeness of the sampling design | |
| Example: Metacognitive strategies as measured in the PISA study | |
| Sampling design | |
| Model-based analysis of data divided into parts | |
| Inclusion of weights in the model | |
| How to assign weights in multilevel models | |
| Appendix. Matrix expressions for the single-level estimators | |
| Glommary | |
| 15. Longitudinal Data | |
| Fixed occasions | |
| The compound symmetry models | |
| Random slopes | |
| The fully multivariate model | |
| Multivariate regression analysis | |
| Explained variance | |
| Variable occasion designs | |
| Populations of curves | |
| Random functions | |
| Explaining the functions | |
| Changing covariates | |
| Autocorrelated residuals | |
| Glommary | |
| 16. Multivariate Multilevel Models | |
| Why analyze multiple dependent variables simultaneously? | |
| The multivariate random intercept model | |
| Multivariate random slope models | |
| Glommary | |
| 17. Discrete Dependent Variables | |
| Hierarchical generalized linear models | |
| Introduction to multilevel logistic regression | |
| Heterogeneous proportions | |
| The logit function: Log-odds | |
| The empty model | |
| The random intercept model | |
| Estimation | |
| Aggregation | |
| Further topics on multilevel logistic regression | |
| Random slope model | |
| Representation as a threshold model | |
| Residual intraclass correlation coefficient | |
| Explained variance | |
| Consequences of adding effects to the model | |
| Ordered categorical variables | |
| Multilevel event history analysis | |
| Multilevel Poisson regression | |
| Glommary | |
| 18. Software | |
| Special software for multilevel modeling | |
| HLM | |
| MLwiN | |
| The MIXOR suite and SuperMix | |
| Modules in general-purpose software packages | |
| SAS procedures VARCOMP, MIXED, GLIMMIX, and NLMIXED | |
| R | |
| Stata | |
| SPSS, commands VARCOMP and MIXED | |
| Other multilevel software | |
| PinT | |
| Optimal Design | |
| MLPowSim | |
| Mplus | |
| Latent Gold | |
| REALCOM | |
| WinBUGS | |
| References | |
| Index |