Multilevel Analysis

Preface second edition Preface to first edition Introduction Multilevel analysis Probability models This book Prerequisites Notation 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 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 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 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 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 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 Heteroscedasticity Heteroscedasticity at level one Linear variance functions Quadratic variance functions Heteroscedasticity at level two Glommary 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 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 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 Other Methods and Models Bayesian inference Sandwich estimators for standard errors Latent class models Glommary 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 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 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 27415.2.4 Changing covariates Autocorrelated residuals Glommary Multivariate Multilevel Models Why analyze multiple dependent variables simultaneously? The multivariate random intercept model Multivariate random slope models Glommary 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 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