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Title: Monte Carlo approximation through Gibbs output in generalized linear mixed models
Authors: Chan, J.S.K.
Kuk, A.Y.C. 
Yam, C.H.K.
Keywords: Generalized linear mixed model
Gibbs sampler
Metropolis-Hastings algorithm
Monte Carlo Newton Raphson
Monte Carlo relative likelihood
Issue Date: Jun-2005
Citation: Chan, J.S.K., Kuk, A.Y.C., Yam, C.H.K. (2005-06). Monte Carlo approximation through Gibbs output in generalized linear mixed models. Journal of Multivariate Analysis 94 (2) : 300-312. ScholarBank@NUS Repository.
Abstract: Geyer (J. Roy. Statist. Soc. 56 (1994) 291) proposed Monte Carlo method to approximate the whole likelihood function. His method is limited to choosing a proper reference point. We attempt to improve the method by assigning some prior information to the parameters and using the Gibbs output to evaluate the marginal likelihood and its derivatives through a Monte Carlo approximation. Vague priors are assigned to the parameters as well as the random effects within the Bayesian framework to represent a non-informative setting. Then the maximum likelihood estimates are obtained through the Newton Raphson method. Thus, out method serves as a bridge between Bayesian and classical approaches. The method is illustrated by analyzing the famous salamander mating data by generalized linear mixed models. © 2004 Elsevier Inc. All rights reserved.
Source Title: Journal of Multivariate Analysis
ISSN: 0047259X
DOI: 10.1016/j.jmva.2004.05.004
Appears in Collections:Staff Publications

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