Multilevel Modeling Using R

Description

Like its bestselling predecessor, Multilevel Modeling Using R, Second Edition provides the reader with a helpful guide to conducting multilevel data modeling using the R software environment. After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single level and multilevel data. New in the Second Edition: Features the use of lmer (instead of lme) and including the most up to date approaches for obtaining confidence intervals for the model parameters. Discusses measures of R2 (the squared multiple correlation coefficient) and overall model fit. Adds a chapter on nonparametric and robust approaches to estimating multilevel models, including rank based, heavy tailed distributions, and the multilevel lasso. Includes a new chapter on multivariate multilevel models. Presents new sections on micro-macro models and multilevel generalized additive models. This thoroughly updated revision gives the reader state-of-the-art tools to launch their own investigations in multilevel modeling and gain insight into their research. About the Authors: W. Holmes Finch is the George and Frances Ball Distinguished Professor of Educational Psychology at Ball State University. Jocelyn E. Bolin is a Professor in the Department of Educational Psychology at Ball State University. Ken Kelley is the Edward F. Sorin Society Professor of IT, Analytics and Operations and the Associate Dean for Faculty and Research for the Mendoza College of Business at the University of Notre Dame. Cover Half Title Title Page Copyright Page Table of Contents Authors 1: Linear Models Simple Linear Regression Estimating Regression Models with Ordinary Least Squares Distributional Assumptions Underlying Regression Coefficient of Determination Inference for Regression Parameters Multiple Regression Example of Simple Linear Regression by Hand Regression in R Interaction Terms in Regression Categorical Independent Variables Checking Regression Assumptions with R Summary 2: An Introduction to Multilevel Data Structure Nested Data and Cluster Sampling Designs Intraclass Correlation Pitfalls of Ignoring Multilevel Data Structure Multilevel Linear Models Random Intercept Random Slopes Centering Basics of Parameter Estimation with MLMs Maximum Likelihood Estimation Restricted Maximum Likelihood Estimation Assumptions Underlying MLMs Overview of Two-Level MLMs Overview of Three-Level MLMs Overview of Longitudinal Designs and Their Relationship to MLMs Summary 3: Fitting Two-Level Models in R Simple (Intercept-Only) Multilevel Models Interactions and Cross-Level Interactions Using R Random Coefficients Models using R Centering Predictors Additional Options Parameter Estimation Method Estimation Controls Comparing Model Fit lme4 and Hypothesis Testing Summary Note 4: Three-Level and Higher Models Defining Simple Three-Level Models Using the lme4 Package Defining Simple Models with More than Three Levels in the lme4 Package Random Coefficients Models with Three or More Levels in the lme4 Package Summary Note 5: Longitudinal Data Analysis Using Multilevel Models The Multilevel Longitudinal Framework Person Period Data Structure Fitting Longitudinal Models Using the lme4 Package Benefits of Using Multilevel Modeling for Longitudinal Analysis Summary Note 6: Graphing Data in Multilevel Contexts Plots for Linear Models Plotting Nested Data Using the Lattice Package Plotting Model Results Using the Effects Package Summary 7: Brief Introduction to Generalized Linear Models Logistic Regression Model for a Dichotomous Outcome Variable Logistic Regression Model for an Ordinal Outcome Variable Multinomial Logistic Regression Models for Count Data Poisson Regression Models for Overdispersed Count Data Summary 8: Multilevel Generalized Linear Models (MGLMs) MGLMs for a Dichotomous Outcome Variable Random Intercept Logistic Regression Random Coefficients Logistic Regression Inclusion of Additional Level-1 and Level-2 Effects in MGLM MGLM for an Ordinal Outcome Variable Random Intercept Logistic Regression MGLM for Count Data Random Intercept Poisson Regression Random Coefficient Poisson Regression Inclusion of Additional Level-2 Effects to the Multilevel Poisson Regression Model Summary 9: Bayesian Multilevel Modeling MCMCglmm for a Normally Distributed Response Variable Including Level-2 Predictors with MCMCglmm User Defined Priors MCMCglmm for a Dichotomous Dependent Variable MCMCglmm for a Count-Dependent Variable Summary 10: Advanced Issues in Multilevel Modeling Robust Statistics in the Multilevel Context Identifying Potential Outliers in Single-Level Data Identifying Potential Outliers in Multilevel Data Identifying Potential Multilevel Outliers Using R Robust and Rank-Based Estimation for Multilevel Models Fitting Robust and Rank-Based Multilevel Models in R Cauchy Slash Contaminated Multilevel Lasso Fitting the Multilevel Lasso in R Multivariate Multilevel Models Multilevel Generalized Additive Models Fitting GAMM using R Predicting Level-2 Outcomes with Level-1 Variables Power Analysis for Multilevel Models Summary References Index