Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood
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Summary
Since their introduction in 1972, generalized linear models (GLMs) have proven useful in the generalization of classical normal models. Presenting methods for fitting GLMs with random effects to data, Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood explores a wide range of applications, including combining information over trials (meta-analysis), analysis of frailty models for survival data, genetic epidemiology, and analysis of spatial and temporal models with correlated errors.
Written by pioneering authorities in the field, this reference provides an introduction to various theories and examines likelihood inference and GLMs. The authors show how to extend the class of GLMs while retaining as much simplicity as possible. By maximizing and deriving other quantities from h-likelihood, they also demonstrate how to use a single algorithm for all members of the class, resulting in a faster algorithm as compared to existing alternatives.
Complementing theory with examples, many of which can be run by using the code supplied on the accompanying CD, this book is beneficial to statisticians and researchers involved in the above applications as well as quality-improvement experiments and missing-data analysis.
Table of Contents
LIST OF NOTATIONS
PREFACE
INTRODUCTION
CLASSICAL LIKELIHOOD THEORY
Definition
Quantities derived from the likelihood
Profile likelihood
Distribution of the likelihood-ratio statistic
Distribution of the MLE and the Wald statistic
Model selection
Marginal and conditional likelihoods
Higher-order approximations
Adjusted profile likelihood
Bayesian and likelihood methods
Jacobian in likelihood methods
GENERALIZED LINEAR MODELS
Linear models
Generalized linear models
Model checking
Examples
QUASI-LIKELIHOOD
Examples
Iterative weighted least squares
Asymptotic inference
Dispersion models
Extended Quasi-likelihood
Joint GLM of mean and dispersion
Joint GLMs for quality improvement
EXTENDED LIKELIHOOD INFERENCES
Two kinds of likelihood
Inference about the fixed parameters
Inference about the random parameters
Optimality in random-parameter estimation
Canonical scale, h-likelihood and joint inference
Statistical prediction
Regression as an extended model
Missing or incomplete-data problems
Is marginal likelihood enough for inference about fixed
parameters?
Summary: likelihoods in extended framework
NORMAL LINEAR MIXED MODELS
Developments of normal mixed linear models
Likelihood estimation of fixed parameters
Classical estimation of random effects
H-likelihood approach
Example
Invariance and likelihood inference
HIERARCHICAL GLMS
HGLMs
H-likelihood
Inferential procedures using h-likelihood
Penalized quasi-likelihood
Deviances in HGLMs
Examples
Choice of random-effect scale
HGLMS WITH STRUCTURED DISPERSION
HGLMs with structured dispersion
Quasi-HGLMs
Examples
CORRELATED RANDOM EFFECTS FOR HGLMS
HGLMs with correlated random effects
Random effects described by fixed L matrices
Random effects described by a covariance matrix
Random effects described by a precision matrix
Fitting and model-checking
Examples
Twin and family data
Ascertainment problem
SMOOTHING
Spline models
Mixed model framework
Automatic smoothing
Non-Gaussian smoothing
RANDOM-EFFECT MODELS FOR SURVIVAL DATA
Proportional-hazard model
Frailty models and the associated h-likelihood
*Mixed linear models with censoring
Extensions
Proofs
DOUBLE HGLMs
DHGLMs
Models for finance data
H-likelihood procedure for fitting DHGLMs
Random effects in the ? component
Examples
FURTHER TOPICS
Model for multivariate responses
Joint model for continuous and binary data
Joint model for repeated measures and survival time
Missing data in longitudinal studies
Denoising signals by imputation
REFERENCE
DATA INDEX
AUTHOR INDEX
SUBJECT INDEX
Editorial Reviews
"… This book provides a comprehensive summary of [the authors' past work]. However, it is much more than that, and even statisticians who do not agree with their approach to inference will find much here of interest. … some instructors might find this to be a useful text for a course on generalized linear models. … there are many ideas that will be useful for students to mull over …"
-A. Agresti (University of Florida), Short Book Reviews
"The book is well written and replete with examples and discussions. With over 500 references, the authors have amassed an enormous amount of information in a single source."
– James W. Hardin, University of South Carolina, in Journal of the American Statistical Association, June 2009, Vol. 104, No. 486
"The book’s material is valuable . . . There are numerous examples and applications, illustrated on the accompanying Genstat CD."
– Hassan S. Bakouch, Tanta University, in Journal of Applied Statistics, September 2007, Vol. 34, No. 7
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