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 Finchis the George and Frances Ball Distinguished Professor of Educational Psychology at Ball State University.
Jocelyn E. Bolinis a Professor in the Department of Educational Psychology at Ball State University.
Ken Kelleyis 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.
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
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
Pitfalls of Ignoring Multilevel Data Structure
Multilevel Linear Models
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
Parameter Estimation Method
Comparing Model fit
Lme4 and hypothesis testing
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
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
6: Graphing Data in Multilevel Contexts
Plots for Linear Models
Plotting Nested Data
Using the Lattice Package
Plotting Model Results using the Effects Package
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
Models for Overdispersed Count data
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
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
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
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
Appendix: An Introduction to R
Running Statistical Analyses in R
Reading Data into R
Types of Data
Additional R Environment Options
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®). 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®). 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®) 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.