- Author
- Year
- 2016
- Title
- Factor analysis models via I-divergence optimization
- Journal
- Psychometrika
- Volume | Issue number
- 81 | 3
- Pages (from-to)
- 702-726
- Number of pages
- 25
- Document type
- Article
- Faculty
- Faculty of Science (FNWI)
- Institute
- Korteweg-de Vries Institute for Mathematics (KdVI)
- Abstract
-
Given a positive definite covariance matrix Σˆ of dimension n, we approximate it with a covariance of the form HH⊤+D, where H has a prescribed number k<n of columns and D>0 is diagonal. The quality of the approximation is gauged by the I-divergence between the zero mean normal laws with covariances Σˆ and HH⊤+D, respectively. To determine a pair (H, D) that minimizes the I-divergence we construct, by lifting the minimization into a larger space, an iterative alternating minimization algorithm (AML) à la Csiszár-Tusnády. As it turns out, the proper choice of the enlarged space is crucial for optimization. The convergence of the algorithm is studied, with special attention given to the case where D is singular. The theoretical properties of the AML are compared to those of the popular EM algorithm for exploratory factor analysis. Inspired by the ECME (a Newton-Raphson variation on EM), we develop a similar variant of AML, called ACML, and in a few numerical experiments, we compare the performances of the four algorithms.
- URL
- go to publisher's site
- Language
- English
- Persistent Identifier
- https://hdl.handle.net/11245/1.536052
- Downloads
-
Spreij_Finesso_Psychometrika_81-3_2016(Final published version)
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