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
