An empirical comparison between grade of membership and principal component analysis

Abstract

It is the purpose of this paper to contribute to the discussion initiated by Wachter about the parallelism between principal component (PC) and a typological grade of membership (GoM) analysis. The author tested empirically the close relationship between both analysis in a low dimensional framework comprising up to nine dichotomous variables and two typologies. Our contribution to the subject is also empirical. It relies on a dataset from a survey which was especially designed to study the reward of skills in the banking sector in Portugal. The statistical data comprise thirty polythomous variables and were decomposed in four typologies using an optimality criterion. The empirical evidence shows a high correlation between the first PC scores and individual GoM scores. No correlation with the remaining PCs was found, however. In addtion to that, the first, PC also proved effective to rank individuals by skill following the particularity of data distribution meanwhile unveiled in GoM analysis.