Since their introduction, hierarchical generalized linear models (HGLMs) have proven useful in various fields by allowing random effects in regression models. Interest in the topic has grown, and various practical analytical tools have been developed. This book summarizes developments within the field and, using data examples, illustrates how to analyse various kinds of data using R. It provides a likelihood approach to advanced statistical modelling including generalized linear models with random effects, survival analysis and frailty models, multivariate HGLMs, factor and structural equation models, robust modelling of random effects, models including penalty and variable selection and hypothesis testing.
This example-driven book is aimed primarily at researchers and graduate students, who wish to perform data modelling beyond the frequentist framework, and especially for those searching for a bridge between Bayesian and frequentist statistics.
Author(s): Youngjo Lee, Lars Ronnegard, Maengseok Noh
Edition: 1
Publisher: Chapman and Hall/;CRC Press
Year: 2017
Language: English
Pages: 334
City: Boca Raton
Contents
Notation
Preface
Introduction
Motivating examples
Regarding criticisms of the h-likelihood
R code
Exercises
GLMs via iterative weighted least squares
Examples
R code
Fisher's classical likelihood
Iterative weighted least squares
Model checking using residual plots
Hat values
Exercises
Inference for models with unobservables
Examples
R code
Likelihood inference for random e ects
Extended likelihood principle
Laplace approximations for the integrals
Street magician
H-likelihood and empirical Bayes
Exercises
HGLMs - from method to algorithm
Examples
R code
IWLS algorithm for interconnected GLMs
IWLS algorithm for augmented GLM
A includes parameters. For instance, splines and the Intrinsic Autore-
IWLS algorithm for HGLMs
Estimation algorithm for a Poisson GLMM
H and D. The updating of the parameters = ( ; v)
Exercises
HGLMs modeling in R
Examples
R code
Exercises
Double HGLMs - using the dhglm package
Model description for DHGLMs
Examples
An extension of linear mixed models via DHGLM
Implementation in the dhglm package
Exercises
Fitting multivariate HGLMs
Examples
Implementation in the mdhglm package
Exercises
Survival analysis
Examples
Competing risk models
Comparison with alternative R procedures
H-likelihood theory for the frailty model
Running the frailtyHL package
Exercises
Joint models
Examples
H-likelihood approach to joint models
(S1) Estimation of xed and random e ects = (
(S2) Estimation of dispersion parameters = ( ; ;
)
Exercises
Further topics
Examples
Variable selections
Examples
Hypothesis testing
Refs
Data Index
Index
