A semiparametric Bayesian approach to generalized partial linear mixed models for longitudinal data

Nian-Sheng Tang and Xing-De Duan

Computational Statistics & Data Analysis, 2012, vol. 56, issue 12, 4348-4365

Abstract: A generalized partial linear mixed model (GPLMM) is a natural extension of generalized linear mixed models (GLMMs) and partial linear models (PLMs). Almost all existing methods for analyzing GPLMMs are developed on the basis of the assumption that random effects are distributed as a fully parametric distribution such as normal distribution. In this paper, we extend the GPLMMs by specifying a Dirichlet process prior for a general distribution of random effects, and propose a semiparametric Bayesian approach by simultaneously utilizing an approximation truncation Dirichlet process prior of the random effects and a P-spline approximation of the smoothing function. By combining the block Gibbs sampler and the Metropolis–Hastings algorithm, a hybrid algorithm is presented for sampling observations from the posterior distribution. A procedure for selecting the degree of the polynomial components in nonparametric approximation using Bayes factor is given via path sampling. Some goodness-of-fit statistics are proposed to evaluate the plausibility of the posited model. Several simulation studies and a real example are presented to illustrate the proposed methodologies.

Keywords: Bayes factor; Dirichlet process prior; Generalized partial linear mixed models; Gibbs sampler; Metropolis–Hastings algorithm; P-spline (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:56:y:2012:i:12:p:4348-4365

DOI: 10.1016/j.csda.2012.03.018

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