Factor analysis models via I-divergence optimization

Lorenzo Finesso () and Peter Spreij ()
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Lorenzo Finesso: IEIIT - CNR
Peter Spreij: Universiteit van Amsterdam

Psychometrika, 2016, vol. 81, issue 3, No 6, 702-726

Abstract: Abstract Given a positive definite covariance matrix $$\widehat{\Sigma }$$ Σ ^ of dimension n, we approximate it with a covariance of the form $$HH^\top +D$$ H H ⊤ + D , where H has a prescribed number $$k 0$$ D > 0 is diagonal. The quality of the approximation is gauged by the I-divergence between the zero mean normal laws with covariances $$\widehat{\Sigma }$$ Σ ^ and $$HH^\top +D$$ H H ⊤ + 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.

Keywords: factor analysis; I-divergence; optimal approximate model; alternating minimization; 62H25; 62B10 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11336-015-9486-5

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