Generalized Linear Models with Random Effects
Unified Analysis via H-likelihood
1st Edition
Published on 1. July 2006
Book
Hardback
416 pages
978-1-58488-631-0 (ISBN)
Description
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.
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.
More details
Series
Language
English
Place of publication
United States
Publishing group
Taylor & Francis Inc
Target group
College/higher education
Professional and scholarly
Researchers and graduate students from statistics and biostatistics, medicine, epidemiology, biology, agriculture, and finance.
Illustrations
54 s/w Abbildungen, 65 s/w Tabellen
65 Tables, black and white; 54 Illustrations, black and white
Dimensions
Height: 229 mm
Width: 152 mm
Weight
703 gr
ISBN-13
978-1-58488-631-0 (9781584886310)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Youngjo Lee | John A. Nelder | Yudi Pawitan
Generalized Linear Models with Random Effects
Unified Analysis via H-likelihood, Second Edition
Book
08/2017
2nd Edition
Chapman & Hall/CRC
€172.50
Shipment within 15-20 days
Persons
Content
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
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