Multilevel Analysis\[5mm] An introduction to basic and advanced\ multilevel modeling\ {\normalsize 2nd edition} {\Large Sage Publishers, 2012}

# Contents

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
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