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Article: Grouped Dirichlet distribution: A new tool for incomplete categorical data analysis

TitleGrouped Dirichlet distribution: A new tool for incomplete categorical data analysis
Authors
KeywordsBeta-Liouville distribution
Data augmentation
Dirichlet distribution
EM algorithm
Grouped Dirichlet distribution
Incomplete categorical data
Issue Date2008
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmva
Citation
Journal Of Multivariate Analysis, 2008, v. 99 n. 3, p. 490-509 How to Cite?
AbstractMotivated by the likelihood functions of several incomplete categorical data, this article introduces a new family of distributions, grouped Dirichlet distributions (GDD), which includes the classical Dirichlet distribution (DD) as a special case. First, we develop distribution theory for the GDD in its own right. Second, we use this expanded family as a new tool for statistical analysis of incomplete categorical data. Starting with a GDD with two partitions, we derive its stochastic representation that provides a simple procedure for simulation. Other properties such as mixed moments, mode, marginal and conditional distributions are also derived. The general GDD with more than two partitions is considered in a parallel manner. Three data sets from a case-control study, a leprosy survey, and a neurological study are used to illustrate how the GDD can be used as a new tool for analyzing incomplete categorical data. Our approach based on GDD has at least two advantages over the commonly used approach based on the DD in both frequentist and conjugate Bayesian inference: (a) in some cases, both the maximum likelihood and Bayes estimates have closed-form expressions in the new approach, but not so when they are based on the commonly-used approach; and (b) even if a closed-form solution is not available, the EM and data augmentation algorithms in the new approach converge much faster than in the commonly-used approach. © 2007 Elsevier Inc. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/59876
ISSN
2015 Impact Factor: 0.857
2015 SCImago Journal Rankings: 1.458
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorNg, KWen_HK
dc.contributor.authorTang, MLen_HK
dc.contributor.authorTan, Men_HK
dc.contributor.authorTian, GLen_HK
dc.date.accessioned2010-05-31T03:59:14Z-
dc.date.available2010-05-31T03:59:14Z-
dc.date.issued2008en_HK
dc.identifier.citationJournal Of Multivariate Analysis, 2008, v. 99 n. 3, p. 490-509en_HK
dc.identifier.issn0047-259Xen_HK
dc.identifier.urihttp://hdl.handle.net/10722/59876-
dc.description.abstractMotivated by the likelihood functions of several incomplete categorical data, this article introduces a new family of distributions, grouped Dirichlet distributions (GDD), which includes the classical Dirichlet distribution (DD) as a special case. First, we develop distribution theory for the GDD in its own right. Second, we use this expanded family as a new tool for statistical analysis of incomplete categorical data. Starting with a GDD with two partitions, we derive its stochastic representation that provides a simple procedure for simulation. Other properties such as mixed moments, mode, marginal and conditional distributions are also derived. The general GDD with more than two partitions is considered in a parallel manner. Three data sets from a case-control study, a leprosy survey, and a neurological study are used to illustrate how the GDD can be used as a new tool for analyzing incomplete categorical data. Our approach based on GDD has at least two advantages over the commonly used approach based on the DD in both frequentist and conjugate Bayesian inference: (a) in some cases, both the maximum likelihood and Bayes estimates have closed-form expressions in the new approach, but not so when they are based on the commonly-used approach; and (b) even if a closed-form solution is not available, the EM and data augmentation algorithms in the new approach converge much faster than in the commonly-used approach. © 2007 Elsevier Inc. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/jmvaen_HK
dc.relation.ispartofJournal of Multivariate Analysisen_HK
dc.subjectBeta-Liouville distributionen_HK
dc.subjectData augmentationen_HK
dc.subjectDirichlet distributionen_HK
dc.subjectEM algorithmen_HK
dc.subjectGrouped Dirichlet distributionen_HK
dc.subjectIncomplete categorical dataen_HK
dc.titleGrouped Dirichlet distribution: A new tool for incomplete categorical data analysisen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0047-259X&volume=99&issue=3&spage= 490&epage=509&date=2008&atitle=Grouped+Dirichlet+Distribution:+A+New+Tool+for+Incomplete+Categorical+Data+Analysisen_HK
dc.identifier.emailNg, KW: kaing@hkucc.hku.hken_HK
dc.identifier.emailTian, GL: gltian@hku.hken_HK
dc.identifier.authorityNg, KW=rp00765en_HK
dc.identifier.authorityTian, GL=rp00789en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.jmva.2007.01.010en_HK
dc.identifier.scopuseid_2-s2.0-38349144584en_HK
dc.identifier.hkuros163557en_HK
dc.identifier.hkuros148990-
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-38349144584&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume99en_HK
dc.identifier.issue3en_HK
dc.identifier.spage490en_HK
dc.identifier.epage509en_HK
dc.identifier.isiWOS:000253821500011-
dc.publisher.placeUnited Statesen_HK
dc.identifier.scopusauthoridNg, KW=7403178774en_HK
dc.identifier.scopusauthoridTang, ML=7401974011en_HK
dc.identifier.scopusauthoridTan, M=7401464906en_HK
dc.identifier.scopusauthoridTian, GL=25621549400en_HK

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