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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. "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

Multilevel Modeling Using R

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 2 level MLMs





Overview of 3 level MLMs





Overview of longitudinal designs and their relationships to MLMs





Summary











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