New Insights into PCA + Varimax for Psychological Researchers: A short commentary on Rohe & Zeng (2022)

Abstract

In their paper “Vintage factor analysis with varimax performs statistical inference”, Rohe and Zeng (R&Z; 2022) demonstrate the usefulness of principal component analysis with varimax rotation (PCA+VR), a combination they call vintage factor analysis. The authors show that PCA+VR can be used to estimate factor scores and factor loadings, if a certain leptokurtic condition is fulfilled that can be assessed by simple visual diagnostics. In a side result, they also imply that PCA+VR is able to estimate factor scores even if the latent factors are correlated. In our commentary, we briefly discuss some implications of these results for psychological research and note that the suggested diagnostics of “radial streaks” might give less clear results in typical psychological applications. The commentary includes extensive electronic supplemental materials, containing a data example and a small simulation on estimating correlated factors, that can be found at https://osf.io/5symf/.

Regularized Exploratory Factor Analysis as an Alternative to Factor Rotation

“…Rohe and Zeng (2022) show that this rotational invariance only occurs for multivariate normal data and that factors that stem from non-normal distributions are partially identifiable, though. Their proposed combination of principal component analysis and Varimax rotation to identify the factors appears to be especially useful for sparse data, but does not seem to be the best way for typical psychological data (Pargent et al, 2023).…”