Epistemological reasons for preferring component analysis to factor analysis

Abstract

Spearman's and Thomson's mathematical controversy over factor theory was forgotten when it became evident that empirical tetrad-differences bound away from zero (and when empirical evidence argued the need for extracting more factors from a matrix). In fact, both their models lead to zero tetraddifferences. Being more interested in the psychological than in the mathematical aspects of Spearman's model. Thompson remained indifferent to mathematical aspects of multiple factor analysis when Thurstone theorized it. Thus, he did not perceive that his counter-example negated the assumption Thrustone shared the rank of the matrix. The idea that components to be extracted must be equal to the rank of the matrix is not assumed in Hotelling's component model: as a result, this is the first epistemological reason for preferring component analysis to factor analysis. A second epistemological reason is the central theorem of Thurstone's multiple-factor model, which can be criticized because it is an assumption that, the rank of a complete matrix being n, it becomes k when commonalities are in the principal diagonal. This assumption goes against common sense, a fact demonstrated through comparison between residuals after k components have been extracted and after k principal factors have been extracted.