Jichuan Wang, Wright State University, Dayton, Ohio, USA; Haiyi Xie, Dartmouth Medical School, Hanover, New Hampshire, USA; James H. Fisher, Wright State University, Dayton, Ohio, USA.

• Preface1 Introduction1.1 Conceptual framework of multilevel modeling1.2 Hierarchically structured data1.3 Variables in multilevel data1.4 Analytical problems with multilevel data1.5 Advantages and limitations of multilevel modeling1.6 Computer software for multilevel modeling2 Basics of Linear Multilevel Models2.1 Intraclass correlation coefficient (ICC)2.2 Formulation of two-level multilevel models2.3 Model assumptions2.4 Fixed and random regression coefficients2.5 Cross-level interactions2.6 Measurement centering2.7 Model estimation2.8 Model fit, hypothesis testing, and model comparisons2.8.1 Model fit2.8.2 Hypothesis testing2.8.3 Model comparisons2.9 Explained level-1 and level-2 variances2.10 Steps for building multilevel models2.11 Higher-level multilevel models3 Application of Two-level Linear Multilevel Models3.1 Data3.2 Empty model3.3 Predicting between-group variation3.4 Predicting within-group variation3.5 Testing random level-1 slopes3.6 Across-level interactions3.7 Other issues in model development4 Application of Multilevel Modeling to Longitudinal Data4.1 Features of longitudinal data4.2 Limitations of traditional approaches for modeling longitudinal data4.3 Advantages of multilevel modeling for longitudinal data4.4 Formulation of growth models4.5 Data description and manipulation4.6 Linear growth models4.6.1 The shape of average outcome change over time4.6.2 Random intercept growth models4.6.3 Random intercept and slope growth models4.6.4 Intercept and slope as outcomes4.6.5 Controlling for individual background variables in models4.6.6 Coding time score4.6.7 Residual variance/covariance structures4.6.8 Time-varying covariates4.7 Curvilinear growth models4.7.1 Polynomial growth model4.7.2 Dealing with collinearity in higher order polynomial growth model4.7.3 Piecewise (linear spline) growth model5 Multilevel Models for Discrete Outcome Measures5.1 Introduction to generalized linear mixed models5.1.1 Generalized linear models5.1.2 Generalized linear mixed models5.2 SAS Procedures for multilevel modeling with discrete outcomes5.3 Multilevel models for binary outcomes5.3.1 Logistic regression models5.3.2 Probit models5.3.3 Unobserved latent variables and observed binary outcome measures5.3.4 Multilevel logistic regression models5.3.5 Application of multilevel logistic regression models5.3.6 Application of multilevel logit models to longitudinal data5.4 Multilevel models for ordinal outcomes5.4.1 Cumulative logit models5.4.2 Multilevel cumulative logit models5.5 Multilevel models for nominal outcomes5.5.1 Multinomial logit models5.5.2 Multilevel multinomial logit models5.5.3 Application of multilevel multinomial logit models5.6 Multilevel models for count outcomes5.6.1 Poisson regression models5.6.2 Poisson regression with over-dispersion and a negativebinomial model5.6.3 Multilevel Poisson and negative binomial models5.6.4 Application of multilevel Poisson and negative binomial models6 Other Applications of Multilevel Modeling and Related Issues6.1 Multilevel zero-inflated models for count data with extra zeros6.1.1 Fixed-effect ZIP model6.1.2 Random effect zero-inflated Poisson (RE-ZIP) models6.1.3 Random effect zero-inflated negative binomial (RE-ZINB) models6.1.4 Application of RE-ZIP and RE-ZINB models6.2 Mixed-effect mixed-distribution models for semi-continuous outcomes6.2.1 Mixed-effects mixed distribution model6.2.2 Application of the Mixed-Effect mixed distribution model6.3 Bootstrap multilevel modeling6.3.1 Nonparametric residual bootstrap multilevel modeling6.3.2 Parametric residual bootstrap multilevel modeling6.3.3 Application of nonparametric residual bootstrap multilevel modeling6.4 Group-based models for longitudinal data analysis6.4.1 Introduction to group-based model6.4.2 Group-based logit model6.4.3 Group-based zero-inflated Poisson (ZIP) model6.4.4 Group-based censored normal models6.5 Missing values issue6.5.1 Missing data mechanisms and their implications6.5.2 Handling missing data in longitudinal data analyses6.6 Statistical power and sample size for multilevel modeling6.6.1 Sample size estimation for two-level designs6.6.2 Sample size estimation for longitudinal data analysisReferenceIndex