Multilevel Models: Applications using SAS®

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.

Table of Contents:
Preface 1 Introduction 1.1 Conceptual framework of multilevel modeling 1.2 Hierarchically structured data 1.3 Variables in multilevel data 1.4 Analytical problems with multilevel data 1.5 Advantages and limitations of multilevel modeling 1.6 Computer software for multilevel modeling 2 Basics of Linear Multilevel Models 2.1 Intraclass correlation coefficient (ICC) 2.2 Formulation of two-level multilevel models 2.3 Model assumptions 2.4 Fixed and random regression coefficients 2.5 Cross-level interactions 2.6 Measurement centering 2.7 Model estimation 2.8 Model fit, hypothesis testing, and model comparisons 2.8.1 Model fit 2.8.2 Hypothesis testing 2.8.3 Model comparisons 2.9 Explained level-1 and level-2 variances 2.10 Steps for building multilevel models 2.11 Higher-level multilevel models 3 Application of Two-level Linear Multilevel Models 3.1 Data 3.2 Empty model 3.3 Predicting between-group variation 3.4 Predicting within-group variation 3.5 Testing random level-1 slopes 3.6 Across-level interactions 3.7 Other issues in model development 4 Application of Multilevel Modeling to Longitudinal Data 4.1 Features of longitudinal data 4.2 Limitations of traditional approaches for modeling longitudinal data 4.3 Advantages of multilevel modeling for longitudinal data 4.4 Formulation of growth models 4.5 Data description and manipulation 4.6 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 covariates 4.7 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 Measures 5.1 Introduction to generalized linear mixed models 5.1.1 Generalized linear models 5.1.2 Generalized linear mixed models 5.2 SAS Procedures for multilevel modeling with discrete outcomes 5.3 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 data 5.4 Multilevel models for ordinal outcomes 5.4.1 Cumulative logit models 5.4.2 Multilevel cumulative logit models 5.5 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 models 5.6 Multilevel models for count outcomes 5.6.1 Poisson regression models 5.6.2 Poisson regression with over-dispersion and a negative binomial 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 Issues 6.1 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 models 6.2 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 model 6.3 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 modeling 6.4 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 models 6.5 Missing values issue 6.5.1 Missing data mechanisms and their implications 6.5.2 Handling missing data in longitudinal data analyses 6.6 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 Reference Index