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| Preface second edition | |
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| Preface to first edition | |
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| Introduction | |
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| Multilevel analysis | |
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| Probability models | |
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| This book | |
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| Prerequisites | |
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| Notation | |
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| Multilevel Theories, Multi-Stage Sampling and Multilevel Models | |
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| Dependence as a nuisance | |
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| Dependence as an interesting phenomenon | |
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| Macro-level, micro-level, and cross-level relations | |
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| Glommary | |
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| Statistical Treatment of Clustered Data | |
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| Aggregation | |
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| Disaggregation | |
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| The intraclass correlation | |
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| Within-group and between group variance | |
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| Testing for group differences | |
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| Design effects in two-stage samples | |
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| Reliability of aggregated variables | |
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| Within-and between group relations | |
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| Regressions | |
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| Correlations | |
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| Estimation of within-and between-group correlations | |
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| Combination of within-group evidence | |
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| Glommary | |
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| The Random Intercept Model | |
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| Terminology and notation | |
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| a regression model: fixed effects only | |
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| Variable intercepts: fixed or random parameters? | |
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| When to use random coefficient models | |
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| Definition of the random intercept model | |
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| More explanatory variables | |
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| Within-and between-group regressions | |
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| Parameter estimation | |
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| 'Estimating' random group effects: posterior means | |
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| Posterior confidence intervals | |
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| Three-level random intercept models | |
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| Glommary | |
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| The Hierarchical Linear Model | |
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| Random slopes | |
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| Heteroscedasticity | |
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| Do not force ?01 to be 0! | |
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| Interpretation of random slope variances | |
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| Explanation of random intercepts and slopes | |
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| Cross-level interaction effects | |
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| a general formulation of fixed and random parts | |
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| Specification of random slope models | |
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| Centering variables with random slopes? | |
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| Estimation | |
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| Three or more levels | |
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| Glommary | |
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| Testing and Model Specification | |
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| Tests for fixed parameters | |
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| Multiparameter tests for fixed effects | |
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| Deviance tests | |
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| More powerful tests for variance parameters | |
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| Other tests for parameters in the random part | |
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| Confidence intervals for parameters in the random part | |
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| Model specification | |
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| Working upward from level one | |
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| Joint consideration of level-one and level-two variables | |
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| Concluding remarks on model specification | |
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| Glommary | |
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| How Much Does the Model Explain? | |
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| Explained variance | |
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| Negative values of R2? | |
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| Definition of the proportion of explained variance in two-level models | |
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| Explained variance in three-level models | |
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| Explained variance in models with random slopes | |
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| Components of variance | |
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| Random intercept models | |
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| Random slope models | |
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| Glommary | |
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| Heteroscedasticity | |
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| Heteroscedasticity at level one | |
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| Linear variance functions | |
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| Quadratic variance functions | |
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| Heteroscedasticity at level two | |
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| Glommary | |
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| Missing Data | |
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| General issues for missing data | |
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| Implications for design | |
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| Missing values of the dependent variable | |
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| Full maximum likelihood | |
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| Imputation | |
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| The imputation method | |
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| Putting together the multiple results | |
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| Multiple imputations by chained equations | |
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| Choice of the imputation model | |
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| Glommary | |
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| Assumptions of the Hierarchical Linear Model | |
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| Assumptions of the hierarchical linear model | |
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| Following the logic of the hierarchical linear model | |
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| Include contextual effects | |
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| Check whether variables have random effects | |
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| Explained variance | |
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| Specification of the fixed part | |
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| Specification of the random part | |
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| Testing for heteroscedasticity | |
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| What to do in case of heteroscedasticity | |
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| Inspection of level-one residuals | |
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| Residuals at level two | |
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| Influence of level-two units | |
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| More general distributional assumptions | |
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| Glommary | |
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| Designing Multilevel Studies | |
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| Some introductory notes on power | |
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| Estimating a population mean | |
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| Measurement of subjects | |
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| Estimating association between variables | |
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| Cross-level interaction effects | |
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| Allocating treatment to groups or individuals | |
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| Exploring the variance structure | |
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| The intraclass correlation | |
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| Variance parameters | |
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| Glommary | |
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| Other Methods and Models | |
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| Bayesian inference | |
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| Sandwich estimators for standard errors | |
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| Latent class models | |
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| Glommary | |
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| Imperfect Hierarchies | |
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| a two-level model with a crossed random factor | |
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| Crossed random effects in three-level models | |
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| Multiple membership models | |
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| Multiple membership multiple classification models | |
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| Glommary | |
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| Survey Weights | |
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| Model-based and design-based inference | |
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| Descriptive and analytic use of surveys | |
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| Two kinds of weights | |
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| Choosing between model-based and design-based analysis | |
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| Inclusion probabilities and two-level weights | |
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| Exploring the informativeness of the sampling design | |
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| Example: Metacognitive strategies as measured in the PISA study | |
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| Sampling design | |
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| Model-based analysis of data divided into parts | |
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| Inclusion of weights in the model | |
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| How to assign weights in multilevel models | |
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| Appendix. Matrix expressions for the single-level estimators | |
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| Glommary | |
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| Longitudinal Data | |
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| Fixed occasions | |
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| The compound symmetry models | |
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| Random slopes | |
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| The fully multivariate model | |
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| Multivariate regression analysis | |
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| Explained variance | |
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| Variable occasion designs | |
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| Populations of curves | |
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| Random functions | |
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| Explaining the functions 27415.2.4 | |
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| Changing covariates | |
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| Autocorrelated residuals | |
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| Glommary | |
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| Multivariate Multilevel Models | |
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| Why analyze multiple dependent variables simultaneously? | |
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| The multivariate random intercept model | |
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| Multivariate random slope models | |
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| Glommary | |
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| Discrete Dependent Variables | |
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| Hierarchical generalized linear models | |
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| Introduction to multilevel logistic regression | |
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| Heterogeneous proportions | |
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| The logit function: Log-odds | |
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| The empty model | |
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| The random intercept model | |
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| Estimation | |
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| Aggregation | |
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| Further topics on multilevel logistic regression | |
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| Random slope model | |
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| Representation as a threshold model | |
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| Residual intraclass correlation coefficient | |
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| Explained variance | |
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| Consequences of adding effects to the model | |
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| Ordered categorical variables | |
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| Multilevel event history analysis | |
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| Multilevel Poisson regression | |
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| Glommary | |
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| Software | |
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| Special software for multilevel modeling | |
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| HLM | |
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| MLwiN | |
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| The MIXOR suite and SuperMix | |
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| Modules in general-purpose software packages | |
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| SAS procedures VARCOMP, MIXED, GLIMMIX, and NLMIXED | |
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| R | |
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| Stata | |
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| SPSS, commands VARCOMP and MIXED | |
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| Other multilevel software | |
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| PinT | |
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| Optimal Design | |
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| MLPowSim | |
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| Mplus | |
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| Latent Gold | |
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| REALCOM | |
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| WinBUGS | |
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| References | |
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| Index | |