THE THEORETICAL FOUNDATIONS OF PRINCIPAL FACTOR ANALYSIS, CANONICAL FACTOR ANALYSIS, AND ALPHA FACTOR ANALYSIS

It is shown that PFA, CFA and AFA are particular cases of a scale-invariant factoring procedure based on variance ratios of certain weighted combinations of variables. Standard derivations in the literature are shown, in contrast, to have unsatisfactory features. It is suggested that the choice between PFA, CFA and AFA involves relatively independent choices of features of each, and that in most cases CFA is to be preferred.