1st Edition

# Multivariate Generalized Linear Mixed Models Using R

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**Multivariate Generalized Linear Mixed Models Using R** presents robust and methodologically sound models for analyzing large and complex data sets, enabling readers to answer increasingly complex research questions. The book applies the principles of modeling to longitudinal data from panel and related studies via the Sabre software package in R.

*A Unified Framework for a Broad Class of Models *The authors first discuss members of the family of generalized linear models, gradually adding complexity to the modeling framework by incorporating random effects. After reviewing the generalized linear model notation, they illustrate a range of random effects models, including three-level, multivariate, endpoint, event history, and state dependence models. They estimate the multivariate generalized linear mixed models (MGLMMs) using either standard or adaptive Gaussian quadrature. The authors also compare two-level fixed and random effects linear models. The appendices contain additional information on quadrature, model estimation, and endogenous variables, along with SabreR commands and examples.

*Improve Your Longitudinal Study*In medical and social science research, MGLMMs help disentangle state dependence from incidental parameters. Focusing on these sophisticated data analysis techniques, this book explains the statistical theory and modeling involved in longitudinal studies. Many examples throughout the text illustrate the analysis of real-world data sets. Exercises, solutions, and other material are available on a supporting website.

**Introduction **

**Generalized Linear Models for Continuous/Interval Scale Data **Introduction

Continuous/interval scale data

Simple and multiple linear regression models

Checking assumptions in linear regression models

Likelihood: multiple linear regression

Comparing model likelihoods

Application of a multiple linear regression model

**Generalized Linear Models for Other Types of Data **Binary data

Ordinal data

Count data

**Family of Generalized Linear Models **Introduction

The linear model

Binary response models

Poisson model

Likelihood

**Mixed Models for Continuous/Interval Scale Data **Introduction

Linear mixed model

The intraclass correlation coefficient

Parameter estimation by maximum likelihood

Regression with level-two effects

Two-level random intercept models

General two-level models including random intercepts

Likelihood

Residuals

Checking assumptions in mixed models

Comparing model likelihoods

Application of a two-level linear model

Two-level growth models

Likelihood

Example on linear growth models

**Mixed Models for Binary Data **Introduction

The two-level logistic model

General two-level logistic models

Intraclass correlation coefficient

Likelihood

Example on binary data

**Mixed Models for Ordinal Data **Introduction

The two-level ordered logit model

Likelihood

Example on mixed models for ordered data

**Mixed Models for Count Data **Introduction

The two-level Poisson model

Likelihood

Example on mixed models for count data

**Family of Two-Level Generalized Linear Models **Introduction

The mixed linear model

Mixed binary response models

Mixed Poisson model

Likelihood

**Three-Level Generalized Linear Models **Introduction

Three-level random intercept models

Three-level generalized linear models

Linear models

Binary response models

Likelihood

Example on three-level generalized linear models

**Models for Multivariate Data **Introduction

Multivariate two-level generalized linear model

Bivariate Poisson model: Example

Bivariate ordered response model: Example

Bivariate linear-probit model: Example

Multivariate two-level generalized linear model likelihood

**Models for Duration and Event History Data **Introduction

Duration data in discrete time

Renewal data

Competing risk data

**Stayers, Non-Susceptibles, and Endpoints **Introduction

Mover-stayer model

Likelihood with mover-stayer model

Example 1: Stayers in Poisson data

Example 2: Stayers in binary data

**Handling Initial Conditions/State Dependence in Binary Data **Introduction to key issues: heterogeneity, state dependence and non-stationarity

Motivational example

Random effects model

Initial conditions problem

Initial treatment of initial conditions problem

Example: Depression data

Classical conditional analysis

Classical conditional model: Depression example

Conditioning on initial response but allowing random effect

*u*to be dependent on

_{0j}*z*

_{j}Wooldridge conditional model: Depression example

Modeling the initial conditions

Same random effect in the initial response and subsequent response models with a common scale parameter

Joint analysis with a common random effect: Depression example

Same random effect in models of the initial response and subsequent responses but with different scale parameters

Joint analysis with a common random effect (different scale parameters): Depression example

Different random effects in models of the initial response and subsequent responses

Different random effects: Depression example

Embedding the Wooldridge approach in joint models for the initial response and subsequent responses

Joint model plus the Wooldridge approach: Depression example

Other link functions

**Incidental Parameters: An Empirical Comparison of Fixed Effects and Random Effects Models**Introduction

Fixed effects treatment of the two-level linear model

Dummy variable specification of the fixed effects model

Empirical comparison of two-level fixed effects and random effects estimators

Implicit fixed effects estimator

Random effects models

Comparing two-level fixed effects and random effects models

Fixed effects treatment of the three-level linear model

**Appendix A: SabreR Installation, SabreR Commands, Quadrature, Estimation, Endogenous EffectsAppendix B: Introduction to R for Sabre**

**Bibliography**

*Exercises appear at the end of most chapters.*

### Biography

**Damon M. Berridge** is a senior lecturer in the Department of Mathematics and Statistics at Lancaster University. Dr. Berridge has nearly 20 years of experience as a statistical consultant. His research focuses on the modeling of binary and ordinal recurrent events through random effects models, with application in medical and social statistics.

**Robert Crouchley** is a professor of applied statistics and director of the Centre for e-Science at Lancaster University. His research interests involve the development of statistical methods and software for causal inference in nonexperimental data. These methods include models for errors in variables, missing data, heterogeneity, state dependence, nonstationarity, event history data, and selection effects.

I think this is a very well organised and written book and therefore I highly recommend it not only to professionals and students but also to applied researchers from many research areas such as education, psychology and economics working on complex and large data sets.

â€”Sebnem Er,Journal of Applied Statistics, 2012