Generalized Linear Models with Random Effects

Generalized Linear Models with Random Effects : Unified Analysis via h-likelihood

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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 more

Product details

  • Hardback | 416 pages
  • 154 x 228 x 28mm | 698.54g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 54 black & white illustrations, 65 black & white tables
  • 1584886315
  • 9781584886310
  • 1,551,659

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 INDEXshow more

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