Should regularization replace simple structure rotation in Exploratory Factor Anal-ysis?

Scharf F, Nestler S

Abstract

Exploratory factor analysis (EFA) is an important tool when the measurement structure of psychological constructs is uncertain. Typically, factor rotation is applied to obtain interpretable results resembling a simple structure. However, an overwhelming multitude of rotation techniques is available of which none is unequivocally superior. Recently, regularization has been suggested as an alternative to factor rotation. In two simulation studies, we addressed the question if regularized EFA is a suitable alternative for rotated EFA. We compared their performance in recovering predefined factor loading patterns with varying amounts of cross-loadings. Elastic net regularized EFA yielded estimates comparable to rotated EFA. For complex loading patterns, both rotated and regularized EFA tended to underestimate cross-loadings and inflate factor correlations, but regularized EFA was able to recover loading patterns as long as a subset of items followed a simple structure. We conclude that regularization is a suitable alternative to factor rotation for psychometric applications.