Some contrasts between maximum likelihood factor analysis and alpha factor analysis

Abstract

The fundamental mathematical model of Thurstone’s common factor analysis is reviewed. The basic covariance matrices of maximum likelihood factor analysis (MLFA) and alpha factor analysis (AFA) are presented. Putting aside the principles on which they are based, these two methods are compared in terms of a number of computational and scaling contrasts following from the application of their respective developments. The paper concludes with a discussion of the number-of-factors problem, the weighting problem in MLFA and AFA, and possible bases for a choice between the two. Index terms: alpha factor analysis, common factor analysis, maximum likelihood factor analysis, number of common factors, scaling and weighting in common factor analysis.