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Article: An efficient MCEM algorithm for fitting generalized linear mixed models for correlated binary data

TitleAn efficient MCEM algorithm for fitting generalized linear mixed models for correlated binary data
Authors
KeywordsCorrelated Binary Data
Data Augmentation
Generalized Linear Mixed Models
Gibbs Sampler
Inverse Bayes Formula
Mcmc
Monte Carlo Em Algorithm
Issue Date2007
PublisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00949655.asp
Citation
Journal Of Statistical Computation And Simulation, 2007, v. 77 n. 11, p. 929-943 How to Cite?
AbstractGeneralized linear mixed models have been widely used in the analysis of correlated binary data arisen in many research areas. Maximum likelihood fitting of these models remains to be a challenge because of the complexity of the likelihood function. Current approaches are primarily to either approximate the likelihood or use a sampling method to find the exact likelihood solution. The former results in biased estimates, and the latter uses Monte Carlo EM (MCEM) methods with a Markov chain Monte Carlo algorithm in each E-step, leading to problems of convergence and slow convergence. This paper develops a new MCEM algorithm to maximize the likelihood for generalized linear mixed probit-normal models for correlated binary data. At each E-step, utilizing the inverse Bayes formula, we propose a direct importance sampling approach (i.e. weighted Monte Carlo integration) to numerically evaluate the first- and the second-order moments of a truncated multivariate normal distribution, thus eliminating problems of convergence and slow convergence. To monitor the convergence of the proposed MCEM, we again employ importance sampling to directly calculate the log-likelihood values and then to plot the difference of the consecutive log-likelihood values against the MCEM iteration. Two real data sets from the children's wheeze study and a three-period crossover trial are analyzed to illustrate the proposed method and for comparison with existing methods. The results show that the new MCEM algorithm outperformed that of McCulloch [McCulloch, C.E., 1994, Maximum likelihood variance components estimation for binary data. Journal of the American Statistical Association, 89, 330-335.] substantially.
Persistent Identifierhttp://hdl.handle.net/10722/172441
ISSN
2015 Impact Factor: 0.749
2015 SCImago Journal Rankings: 0.662
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorTan, Men_US
dc.contributor.authorTian, GLen_US
dc.contributor.authorFang, HBen_US
dc.date.accessioned2012-10-30T06:22:33Z-
dc.date.available2012-10-30T06:22:33Z-
dc.date.issued2007en_US
dc.identifier.citationJournal Of Statistical Computation And Simulation, 2007, v. 77 n. 11, p. 929-943en_US
dc.identifier.issn0094-9655en_US
dc.identifier.urihttp://hdl.handle.net/10722/172441-
dc.description.abstractGeneralized linear mixed models have been widely used in the analysis of correlated binary data arisen in many research areas. Maximum likelihood fitting of these models remains to be a challenge because of the complexity of the likelihood function. Current approaches are primarily to either approximate the likelihood or use a sampling method to find the exact likelihood solution. The former results in biased estimates, and the latter uses Monte Carlo EM (MCEM) methods with a Markov chain Monte Carlo algorithm in each E-step, leading to problems of convergence and slow convergence. This paper develops a new MCEM algorithm to maximize the likelihood for generalized linear mixed probit-normal models for correlated binary data. At each E-step, utilizing the inverse Bayes formula, we propose a direct importance sampling approach (i.e. weighted Monte Carlo integration) to numerically evaluate the first- and the second-order moments of a truncated multivariate normal distribution, thus eliminating problems of convergence and slow convergence. To monitor the convergence of the proposed MCEM, we again employ importance sampling to directly calculate the log-likelihood values and then to plot the difference of the consecutive log-likelihood values against the MCEM iteration. Two real data sets from the children's wheeze study and a three-period crossover trial are analyzed to illustrate the proposed method and for comparison with existing methods. The results show that the new MCEM algorithm outperformed that of McCulloch [McCulloch, C.E., 1994, Maximum likelihood variance components estimation for binary data. Journal of the American Statistical Association, 89, 330-335.] substantially.en_US
dc.languageengen_US
dc.publisherTaylor & Francis Ltd. The Journal's web site is located at http://www.tandf.co.uk/journals/titles/00949655.aspen_US
dc.relation.ispartofJournal of Statistical Computation and Simulationen_US
dc.subjectCorrelated Binary Dataen_US
dc.subjectData Augmentationen_US
dc.subjectGeneralized Linear Mixed Modelsen_US
dc.subjectGibbs Sampleren_US
dc.subjectInverse Bayes Formulaen_US
dc.subjectMcmcen_US
dc.subjectMonte Carlo Em Algorithmen_US
dc.titleAn efficient MCEM algorithm for fitting generalized linear mixed models for correlated binary dataen_US
dc.typeArticleen_US
dc.identifier.emailTian, GL: gltian@hku.hken_US
dc.identifier.authorityTian, GL=rp00789en_US
dc.description.naturelink_to_subscribed_fulltexten_US
dc.identifier.doi10.1080/10629360600843153en_US
dc.identifier.scopuseid_2-s2.0-35649023287en_US
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-35649023287&selection=ref&src=s&origin=recordpageen_US
dc.identifier.volume77en_US
dc.identifier.issue11en_US
dc.identifier.spage929en_US
dc.identifier.epage943en_US
dc.identifier.isiWOS:000252359600002-
dc.publisher.placeUnited Kingdomen_US
dc.identifier.scopusauthoridTan, M=7401464681en_US
dc.identifier.scopusauthoridTian, GL=25621549400en_US
dc.identifier.scopusauthoridFang, HB=7402543028en_US
dc.identifier.citeulike3198296-

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