An Empirical Comparison between Grade of Membership and Principal Component Analysis

Abstract

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