An introduction to basic and advanced

multilevel modeling

2nd edition

Sage Publishers, 2012

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 |