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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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Semiparametric Mixed Models for Longitudinal Data

Semiparametric Mixed Models for Longitudinal Data

Chapter:
(p.178) 4 Semiparametric Mixed Models for Longitudinal Data
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/9780199533022.003.0004

This chapter considers Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. Section 4.1 assumes Gaussian smoothness priors, focusing on Bayesian P-splines in combination with Gaussian priors for random effects, and outlines various model specifications that are included as special cases in SPMMs. Section 4.2 describes inferential techniques, detailing both empirical Bayes estimation based on mixed model technology and full Bayes techniques. Section 4.3 discusses the relation between Bayesian smoothing and correlation. Section 4.4 considers some additional or alternative semiparametric extensions of generalized linear mixed models: First, as in Section 3.2, the assumption of Gaussian random effects can be removed by allowing nonparametric Dirichlet process or Dirichlet process mixture priors in combination with Gaussian smoothness priors for functional effects. Second, local adaptivity of functional effects can be improved by scale mixtures of Gaussian smoothness priors, with variance parameters following stochastic process priors in another hierarchical stage. Third, the case of high-dimensional fixed effects β is also considered, with Bayesian shrinkage priors regularizing the resulting ill-posed inferential problem. Shrinkage priors can also be used for model choice and variable selection. The final Section 4.5 describes strategies for model choice and model checking in SPMMs.

Keywords:   semiparametric mixed models, Bayesian P-splines, Bayesian inference, Gaussian smoothness priors, Dirichlet process, generalized linear mixed models

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