Fitting the factor analysis model in ℓ1 norm

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 ?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.