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Fitting the factor analysis model in ℓ 1 norm
Author(s) -
Trendafilov Nickolay T.
Publication year - 2005
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.2005.tb00313.x
Subject(s) - positive definiteness , mathematics , factor (programming language) , exploratory factor analysis , norm (philosophy) , matrix norm , matrix (chemical analysis) , goodness of fit , factor analysis , measure (data warehouse) , mathematical optimization , positive definite matrix , computer science , statistics , eigenvalues and eigenvectors , physics , materials science , structural equation modeling , quantum mechanics , political science , law , composite material , programming language , database
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 ℓ 1 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.