Article: ML estimation for factor analysis: EM or non-EM?
| Title | ML estimation for factor analysis: EM or non-EM? |
|---|---|
| Authors | Zhao, JH1 3 Yu, PLH1 Jiang, Q2 |
| Keywords | CM ECME EM Factor analysis Maximum likelihood estimation |
| Issue Date | 2008 |
| Publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0960-3174 |
| Citation | Statistics And Computing, 2008, v. 18 n. 2, p. 109-123 [How to Cite?] DOI: http://dx.doi.org/10.1007/s11222-007-9042-y |
| Abstract | To 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. |
| ISSN | 0960-3174 2011 Impact Factor: 1.429 2011 SCImago Journal Rankings: 0.093 |
| DOI | http://dx.doi.org/10.1007/s11222-007-9042-y |
| References | References in Scopus |
| dc.contributor.author | Zhao, JH |
|---|---|
| dc.contributor.author | Yu, PLH |
| dc.contributor.author | Jiang, Q |
| dc.date.accessioned | 2010-09-06T08:33:45Z |
| dc.date.available | 2010-09-06T08:33:45Z |
| dc.date.issued | 2008 |
| dc.description.abstract | To 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.nature | Link_to_subscribed_fulltext |
| dc.identifier.citation | Statistics 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.citeulike | 10318479 |
| dc.identifier.doi | http://dx.doi.org/10.1007/s11222-007-9042-y |
| dc.identifier.epage | 123 |
| dc.identifier.hkuros | 145601 |
| dc.identifier.issn | 0960-3174 2011 Impact Factor: 1.429 2011 SCImago Journal Rankings: 0.093 |
| dc.identifier.issue | 2 |
| dc.identifier.openurl | ![]() |
| dc.identifier.scopus | eid_2-s2.0-41549124138 |
| dc.identifier.spage | 109 |
| dc.identifier.uri | http://hdl.handle.net/10722/82818 |
| dc.identifier.volume | 18 |
| dc.language | eng |
| dc.publisher | Springer New York LLC. The Journal's web site is located at http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0960-3174 |
| dc.publisher.place | United States |
| dc.relation.ispartof | Statistics and Computing |
| dc.relation.references | References in Scopus |
| dc.subject | CM |
| dc.subject | ECME |
| dc.subject | EM |
| dc.subject | Factor analysis |
| dc.subject | Maximum likelihood estimation |
| dc.title | ML estimation for factor analysis: EM or non-EM? |
| dc.type | Article |
Author Affiliations
- The University of Hong Kong
- Southeast University
- Yunnan University


