Generalized Linear Models with Random Effects: Unified Analysis via H-likelihood
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.
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Correlated random effects for HGLMs
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adjusted profile likelihood algorithm analysis approximation assumed assumption B-spline Bayesian binomial canonical scale Chapter classical likelihood component GLMs compute consider correlation covariates defined density deviance DHGLM dispersion model dispersion parameters distribution example exponential family extended likelihood Fisher information fixed effects fixed parameters formula frailty models gamma given gives GLM family GLMMs h-likelihood h-likelihood method h-loglihood hazard function HGLM interval joint maximization Laplace approximation Lee and Nelder likelihood function likelihood inferences likelihood principle linear mixed model linear model linear predictor marginal likelihood mean model ML estimator normal normal distribution nuisance parameters observed overdispersion plots precision matrix procedure quasi-likelihood random components random effects random parameters random-effect model regression residuals response sample shows smoothing statistical structured dispersion Suppose Table term values variables variance function vector Ymis yobs