An Empirical Comparison between Grade of Membership and Principal Component Analysis

Document Type : Research Paper


Department of Quantitative Methods, Instituto Universitario de Lisboa (ISCTE - IUL), BRU-UNIDE, Av. Forcas Armadas, Lisbon, Portugal


t 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.


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