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Fitting the factor analysis model in ℓ1 norm

Trendafilov, Nickolay T. (2005). Fitting the factor analysis model in ℓ1 norm. British Journal of Mathematical and Statistical Psychology, 58(1) pp. 19–31.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1348/000711005X47168
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Abstract

The well-known problem of fitting the exploratory factor analysis model is reconsidered where the usual least squares goodness-of-fit function is replaced by a more resistant discrepancy measure, based on a smooth approximation of the ℓ1 norm. Fitting the factor analysis model to the sample correlation matrix is a complex matrix optimization problem which requires the structure preservation of the unknown parameters (e.g. positive definiteness). The projected gradient approach is a natural way of solving such data matching problems as especially designed to follow the geometry of the model parameters. Two reparameterizations of the factor analysis model are considered. The approach leads to globally convergent procedures for simultaneous estimation of the factor analysis matrix parameters. Numerical examples illustrate the algorithms and factor analysis solutions.

Item Type: Journal Article
Copyright Holders: 2005 The British Psychological Society
ISSN: 0007-1102
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 22564
Depositing User: Sarah Frain
Date Deposited: 17 Aug 2010 13:40
Last Modified: 02 Dec 2010 21:01
URI: http://oro.open.ac.uk/id/eprint/22564
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