Multilevel Models

Interest in multilevel statistical models for social science and public health studies has been aroused dramatically since the mid-1980s. New multilevel modeling techniques are giving researchers tools for analyzing data that have a hierarchical or clustered structure. Multilevel models are now applied to a wide range of studies in sociology, population studies, education studies, psychology, economics, epidemiology, and public health. This book covers a broad range of topics about multilevel modeling. The goal of the authors is to help students and researchers who are interested in analysis of multilevel data to understand the basic concepts, theoretical frameworks and application methods of multilevel modeling. The book is written in non-mathematical terms, focusing on the methods and application of various multilevel models, using the internationally widely used statistical software, the Statistics Analysis System (SAS®). Examples are drawn from analysis of real-world research data. The authors focus on twolevel models in this book because it is most frequently encountered situation in real research. These models can be readily expanded to models with three or more levels when applicable. A wide range of linear and non-linear multilevel models are introduced and demonstrated.

Auteur

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.

Contenu
Preface 1 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 modeling 2 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 comparisons 2.8.1 Model fit 2.8.2 Hypothesis testing 2.8.3 Model comparisons2.9 Explained level-1 and level-2 variances2.10 Steps for building multilevel models2.11 Higher-level multilevel models 3 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 development 4 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 models 4.6.1 The shape of average outcome change over time 4.6.2 Random intercept growth models 4.6.3 Random intercept and slope growth models 4.6.4 Intercept and slope as outcomes 4.6.5 Controlling for individual background variables in models 4.6.6 Coding time score 4.6.7 Residual variance/covariance structures 4.6.8 Time-varying covariates4.7 Curvilinear growth models 4.7.1 Polynomial growth model 4.7.2 Dealing with collinearity in higher order polynomial growth model 4.7.3 Piecewise (linear spline) growth model 5 Multilevel Models for Discrete Outcome Measures5.1 Introduction to generalized linear mixed models 5.1.1 Generalized linear models 5.1.2 Generalized linear mixed models5.2 SAS Procedures for multilevel modeling with discrete outcomes5.3 Multilevel models for binary outcomes 5.3.1 Logistic regression models 5.3.2 Probit models 5.3.3 Unobserved latent variables and observed binary outcome measures 5.3.4 Multilevel logistic regression models 5.3.5 Application of multilevel logistic regression models 5.3.6 Application of multilevel logit models to longitudinal data5.4 Multilevel models for ordinal outcomes 5.4.1 Cumulative logit models 5.4.2 Multilevel cumulative logit models5.5 Multilevel models for nominal outcomes 5.5.1 Multinomial logit models 5.5.2 Multilevel multinomial logit models 5.5.3 Application of multilevel multinomial logit models5.6 Multilevel models for count outcomes 5.6.1 Poisson regression models 5.6.2 Poisson regression with over-dispersion and a negativebinomial model 5.6.3 Multilevel Poisson and negative binomial models 5.6.4 Application of multilevel Poisson and negative binomial models 6 Other Applications of Multilevel Modeling and Related Issues6.1 Multilevel zero-inflated models for count data with extra zeros 6.1.1 Fixed-effect ZIP model 6.1.2 Random effect zero-inflated Poisson (RE-ZIP) models 6.1.3 Random effect zero-inflated negative binomial (RE-ZINB) models 6.1.4 Application of RE-ZIP and RE-ZINB models6.2 Mixed-effect mixed-distribution models for semi-continuous outcomes 6.2.1 Mixed-effects mixed distribution model 6.2.2 Application of the Mixed-Effect mixed distribution model6.3 Bootstrap multilevel modeling 6.3.1 Nonparametric residual bootstrap multilevel modeling 6.3.2 Parametric residual bootstrap multilevel modeling 6.3.3 Application of nonparametric residual bootstrap multilevel modeling6.4 Group-based models for longitudinal data analysis 6.4.1 Introduction to group-based model 6.4.2 Group-based logit model 6.4.3 Group-based zero-inflated Poisson (ZIP) model 6.4.4 Group-based censored normal models6.5 Missing values issue 6.5.1 Missing data mechanisms and their implications 6.5.2 Handling missing data in longitudinal data analyses6.6 Statistical power and sample size for multilevel modeling 6.6.1 Sample size estimation for two-level designs 6.6.2 Sample size estimation for longitudinal data analysis ReferenceIndex