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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 | |
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