Article: ML estimation for factor analysis: EM or non-EM?

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TitleML estimation for factor analysis: EM or non-EM?
AuthorsZhao, JH1 3
Yu, PLH1
Jiang, Q2
KeywordsCM
ECME
EM
Factor analysis
Maximum likelihood estimation
Issue Date2008
PublisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0960-3174
CitationStatistics And Computing, 2008, v. 18 n. 2, p. 109-123 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s11222-007-9042-y
AbstractTo obtain maximum likelihood (ML) estimation in factor analysis (FA), we propose in this paper a novel and fast conditional maximization (CM) algorithm, which has quadratic and monotone convergence, consisting of a sequence of CM log-likelihood (CML) steps. The main contribution of this algorithm is that the closed form expression for the parameter to be updated in each step can be obtained explicitly, without resorting to any numerical optimization methods. In addition, a new ECME algorithm similar to Liu's (Biometrika 81, 633-648, 1994) one is obtained as a by-product, which turns out to be very close to the simple iteration algorithm proposed by Lawley (Proc. R. Soc. Edinb. 60, 64-82, 1940) but our algorithm is guaranteed to increase log-likelihood at every iteration and hence to converge. Both algorithms inherit the simplicity and stability of EM but their convergence behaviors are much different as revealed in our extensive simulations: (1) In most situations, ECME and EM perform similarly; (2) CM outperforms EM and ECME substantially in all situations, no matter assessed by the CPU time or the number of iterations. Especially for the case close to the well known Heywood case, it accelerates EM by factors of around 100 or more. Also, CM is much more insensitive to the choice of starting values than EM and ECME. © 2007 Springer Science+Business Media, LLC.
ISSN0960-3174
2011 Impact Factor: 1.429
2011 SCImago Journal Rankings: 0.093
DOIhttp://dx.doi.org/10.1007/s11222-007-9042-y
ReferencesReferences in Scopus
DC Field
Value
dc.contributor.authorZhao, JH
dc.contributor.authorYu, PLH
dc.contributor.authorJiang, Q
dc.date.accessioned2010-09-06T08:33:45Z
dc.date.available2010-09-06T08:33:45Z
dc.date.issued2008
dc.description.abstractTo obtain maximum likelihood (ML) estimation in factor analysis (FA), we propose in this paper a novel and fast conditional maximization (CM) algorithm, which has quadratic and monotone convergence, consisting of a sequence of CM log-likelihood (CML) steps. The main contribution of this algorithm is that the closed form expression for the parameter to be updated in each step can be obtained explicitly, without resorting to any numerical optimization methods. In addition, a new ECME algorithm similar to Liu's (Biometrika 81, 633-648, 1994) one is obtained as a by-product, which turns out to be very close to the simple iteration algorithm proposed by Lawley (Proc. R. Soc. Edinb. 60, 64-82, 1940) but our algorithm is guaranteed to increase log-likelihood at every iteration and hence to converge. Both algorithms inherit the simplicity and stability of EM but their convergence behaviors are much different as revealed in our extensive simulations: (1) In most situations, ECME and EM perform similarly; (2) CM outperforms EM and ECME substantially in all situations, no matter assessed by the CPU time or the number of iterations. Especially for the case close to the well known Heywood case, it accelerates EM by factors of around 100 or more. Also, CM is much more insensitive to the choice of starting values than EM and ECME. © 2007 Springer Science+Business Media, LLC.
dc.description.natureLink_to_subscribed_fulltext
dc.identifier.citationStatistics And Computing, 2008, v. 18 n. 2, p. 109-123 [How to Cite?]
DOI: http://dx.doi.org/10.1007/s11222-007-9042-y
dc.identifier.citeulike10318479
dc.identifier.doihttp://dx.doi.org/10.1007/s11222-007-9042-y
dc.identifier.epage123
dc.identifier.hkuros145601
dc.identifier.issn0960-3174
2011 Impact Factor: 1.429
2011 SCImago Journal Rankings: 0.093
dc.identifier.issue2
dc.identifier.openurl
dc.identifier.scopuseid_2-s2.0-41549124138
dc.identifier.spage109
dc.identifier.urihttp://hdl.handle.net/10722/82818
dc.identifier.volume18
dc.languageeng
dc.publisherSpringer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0960-3174
dc.publisher.placeUnited States
dc.relation.ispartofStatistics and Computing
dc.relation.referencesReferences in Scopus
dc.subjectCM
dc.subjectECME
dc.subjectEM
dc.subjectFactor analysis
dc.subjectMaximum likelihood estimation
dc.titleML estimation for factor analysis: EM or non-EM?
dc.typeArticle
Author Affiliations
  1. The University of Hong Kong
  2. Southeast University
  3. Yunnan University