Should regularization replace simple structure rotation in Exploratory Factor Analysis?

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Description: Exploratory factor analysis (EFA) is an important statistical tool when the measurement structure of psychological constructs is uncertain. Typically, factor rotation is applied to obtain more interpretable results resembling a simple structure. However, researchers are overwhelmed by the multitude of available rotation techniques of which none is unequivocally superior. Regularized EFA has been suggested as an alternative to factor rotation. In two simulation studies, we address the question if regularized EFA is a suitable alternative for rotated EFA in typical psychometric application scenarios, such as questionnaire development. We compared the performance of factor rotation and regularization in recovering pre-defined factor loading patterns with varying amounts of cross-loadings. The results showed that elastic net regularized EFA yields estimates comparable to rotated EFA. For complex factor loading patterns, both rotated and regularized EFA tended to underestimate cross-loadings and inflate factor correlations but regularized EFA was able to recover factor 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.

License: CC-By Attribution 4.0 International

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This project contains supplementary material, data, and R scripts in order to reproduce the results from the manuscript "Should regularization replace simple structure rotation in Exploratory Factor Analysis?" (accepted for publication in Structural Equation Modeling: A Multidisciplinary Journal). In Condition_Complex2.pdf, we report the results of an additional simulation condition that we invest...

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