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Multilevel Modeling Using R


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Table of Contents

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


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


Basics of Parameter Estimation with MLMs

Maximum Likelihood Estimation

Restricted Maximum Likelihood Estimation

Assumptions Underlying MLMs

Overview of 2 level MLMs

Overview of 3 level MLMs

Overview of longitudinal designs and their relationships to MLMs


3: Fitting 2-level Models

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 4: 3 Level and Higher Models Defining simple 3-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 5: Longitudinal Data Analysis using Multilevel Models The Multilevel Longitudinal Framework Person Period Data Structure Fitting Longitudinal Models using the lme4 package Changing the Covariance Structure of Longitudinal Models Benefits of Multilevel Modeling for Longitudinal Analysis Summary 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 (MGLM) MGLMs for a Dichotomous Outcome Variable Random Intercept Logistic Regression Random Coefficient Logistic Regression Inclusion of Additional level 1 and level 2 effects in MGLM MLGM 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 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 Appendix: An Introduction to R Running Statistical Analyses in R Reading Data into R Missing Data Types of Data Additional R Environment Options

About the Author

W. Holmes Finch is a professor in the Department of Educational Psychology at Ball State University, where he teaches courses on factor analysis, structural equation modeling, categorical data analysis, regression, multivariate statistics, and measurement to graduate students in psychology and education. Dr. Finch is also an Accredited Professional Statistician (PStat (R)). He earned a PhD from the University of South Carolina. His research interests include multilevel models, latent variable modeling, methods of prediction and classification, and nonparametric multivariate statistics. Jocelyn E. Bolin is an assistant professor in the Department of Educational Psychology at Ball State University, where she teaches courses on introductory and intermediate statistics, multiple regression analysis, and multilevel modeling to graduate students in social science disciplines. Dr. Bolin is a member of the American Psychological Association, the American Educational Research Association, and the American Statistical Association and is an Accredited Professional Statistician (PStat (R)). She earned a PhD in educational psychology from Indiana University Bloomington. Her research interests include statistical methods for classification and clustering and use of multilevel modeling in the social sciences. Ken Kelley is the Viola D. Hank Associate Professor of Management in the Mendoza College of Business at the University of Notre Dame. Dr. Kelley is also an Accredited Professional Statistician (PStat (R)) and associate editor of Psychological Methods. His research involves the development, improvement, and evaluation of quantitative methods, especially as they relate to statistical and measurement issues in applied research. He is the developer of the MBESS package for the R statistical language and environment.

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