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INFERENCE IN DIRICHLET PROCESS MIXED GENERALIZED LINEAR MODELS BY USING MONTE CARLO EM
Author(s) -
Naskar Malay,
Das Kalyan
Publication year - 2004
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/j.1467-842x.2004.00363.x
Subject(s) - mathematics , gibbs sampling , generalized linear mixed model , overdispersion , dirichlet distribution , dirichlet process , generalized linear model , hierarchical dirichlet process , consistency (knowledge bases) , quasi likelihood , mixture model , generalized dirichlet distribution , statistics , mathematical optimization , count data , bayesian probability , poisson distribution , mathematical analysis , dirichlet's energy , geometry , boundary value problem
Summary Generalized linear mixed models are widely used for describing overdispersed and correlated data. Such data arise frequently in studies involving clustered and hierarchical designs. A more flexible class of models has been developed here through the Dirichlet process mixture. An additional advantage of using such mixture models is that the observations can be grouped together on the basis of the overdispersion present in the data. This paper proposes a partial empirical Bayes method for estimating all the model parameters by adopting a version of the EM algorithm. An augmented model that helps to implement an efficient Gibbs sampling scheme, under the non‐conjugate Dirichlet process generalized linear model, generates observations from the conditional predictive distribution of unobserved random effects and provides an estimate of the average number of mixing components in the Dirichlet process mixture. A simulation study has been carried out to demonstrate the consistency of the proposed method. The approach is also applied to a study on outdoor bacteria concentration in the air and to data from 14 retrospective lung‐cancer studies.