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Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data$
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Ludwig Fahrmeir and Thomas Kneib

Print publication date: 2011

Print ISBN-13: 9780199533022

Published to Oxford Scholarship Online: September 2011

DOI: 10.1093/acprof:oso/9780199533022.001.0001

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Generalized Linear Mixed Models

Generalized Linear Mixed Models

Chapter:
(p.107) 3 Generalized Linear Mixed Models
Source:
Bayesian Smoothing and Regression for Longitudinal, Spatial and Event History Data
Author(s):

Ludwig Fahrmeir

Thomas Kneib

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199533022.003.0003

This chapter gives an introduction to linear and generalized linear mixed models. The primary goal is to describe concepts for statistical modelling and inference in this class of models that are needed as basic building blocks or inferential tools in the following chapters. It first describes linear mixed models (LMM) for longitudinal data with (conditionally) Gaussian responses yij , making the conventional assumption that the random effects are i. i. d. Gaussian variables. It then extends LMMs by allowing correlated Gaussian random effects. This leads to a very broad class of models that are appropriate for analysing spatial and spatio-temporal data and for Bayesian approaches to semiparametric smoothing. Section 3.2 introduces LMMs with flexible non-Gaussian priors for random effects. In particular, it describes nonparametric modelling of random effects distributions through Dirichlet process-based priors. Section 3.3 provides extensions of LMMs to generalized linear mixed models for non-Gaussian and categorical responses.

Keywords:   linear mixed models, Gaussian random effects, semiparametric smoothing, non-Gaussian priors, Dirichlet processes

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