Bayesian Factor Analysis for Obtaining Simplimax Solutions with an Unspecified Number of Zeros

Abstract

A Bayesian factor analysis procedure is proposed for obtaining a simple loading matrix based on prior information in which the loading matrix approximates a sparse target matrix including zero elements. A feature of this procedure is that the target matrix is unknown and estimated; the number and locations of zero elements are not specified. We derive the estimation of the full conditional distributions of parameters using Gibbs sampling. A simulation study and real data examples demonstrate that the proposed procedure can provide simpler loading matrices than existing rotation methods.