Caveat in abstract factor analysis-based pseudorank estimation Original Research Article

Pseudorank estimation is a ubiquitous problem in multivariate data analysis. Many pseudorank estimation methods currently in use are based on the size of the eigenvalues calculated in abstract factor analysis (AFA). The basic assumption behind these methods is that the eigenvalues, when ordered according to their size, form two distinct sets, namely the so-called primary eigenvalues, that explain the systematic variation in the data together with embedded error, and the so-called secondary eigenvalues, that consist only of noise. This paper shows that a strict separation of eigenvalues in a primary and secondary set can not be expected a priori if the noise in the data is heteroscedastic. The main conclusion is that proper data pre-treatment is required to facilitate AFA-based pseudorank estimation.