An Empirical Comparison between Grade of Membership and Principal Component Analysis

t is the purpose of this paper to contribute to the discussion initiated byWachter about the parallelism between principal component (PC) and atypological grade of membership (GoM) analysis. The author testedempirically the close relationship between both analysis in a lowdimensional framework comprising up to nine dichotomous variables and twotypologies. Our contribution to the subject is also empirical. It relies ona dataset from a survey which was especially designed to study the reward ofskills in the banking sector in Portugal. The statistical data comprisethirty polythomous variables and were decomposed in four typologies using anoptimality criterion. The empirical evidence shows a high correlationbetween the first PC scores and individual GoM scores. No correlation withthe remaining PCs was found, however. In addtion to that, the first PC alsoproved effective to rank individuals by skill following the particularity ofdata distribution meanwhile unveiled in GoM analysis.