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: https://doi.org/10.1348/000711005X47168

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.

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About

• Item ORO ID
• 22564
• Item Type
• Journal Item
• ISSN
• 0007-1102
• Academic Unit or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2005 The British Psychological Society
• Depositing User
• Sarah Frain