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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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PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). (c) Copyright Oxford University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 23 April 2021

Generalized Linear Mixed Models

Generalized Linear Mixed Models

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

Ludwig Fahrmeir (Contributor Webpage)

Thomas Kneib (Contributor Webpage)

Oxford University Press

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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