Multilevel Modeling Using R  book cover
2nd Edition

Multilevel Modeling Using R

ISBN 9781138480674
Published May 20, 2019 by Chapman and Hall/CRC
252 Pages

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Book 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.


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


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

Poisson Regression

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

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


Appendix: An Introduction to R

Running Statistical Analyses in R

Reading Data into R

Missing Data

Types of Data

Additional R Environment Options

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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.


"This book is the second edition of a hugely popular title on multilevel modelling (MLM) using R software. Assuming a basic understanding of how a linear regression model works, if someone is looking for a complete reference on how to fit multilevel models with R, then look no further. Even for those not accustomed to the mathematical details of regression modelling, the provided overview with practical examples and R code should get one up to speed. This book is concise, to the point, and a hands-on, how-to reference on multilevel modelling. Through their clear writing style, the authors have provided answers to all of the essential questions a practitioner might have in fitting a multilevel model. In essence, the book presents straightforward explanations of basic MLM, multilevel generalized linear models, Bayesian multilevel modelling, multivariate multilevel modelling, and how to fit them using R."
- Enayet Raheem, ISCB News, July 2020