LAUSR

When conducting an exploratory factor analysis (EFA), researchers often perform factor rotations using automatic (computerized) algorithms–-such as varimax and oblimin–-to locate psychologically compelling factor patterns. Although it has been known for many years that popular rotation algorithms can converge to local minima when initiated from different starting points (Browne, 2001; Hattori et al., 2017; Rozeboom, 1992), this issue is not widely recognized in the methodological community. Thus, to better understand the causes and consequences of rotation local minima, and to draw further attention to this neglected issue, we investigated the prevalence and correlates of rotation local minima of five factor rotation algorithms: varimax, oblimin, entropy, and geomin (for both orthogonal and oblique rotations). In total, we simulated 16,000 data sets and performed more than 57 million factor rotations to examine the influence of (a) factor loading size, (b) number of factor indicators, (c) factor cross loadings, (d) factor correlation size, (e) model approximation error, (f) sample size, and (g) factor loading standardization on the frequency of local minima in factor rotations. Across three studies, all five rotation methods converged to local solutions under some conditions with geomin (orthogonal and oblique) producing the highest number of local minima among the studied algorithms. Follow-up analyses revealed that when factor rotations produced multiple solutions, the factor pattern with the maximum hyperplane count (operationalized as the number of near zero loadings)–-rather than the lowest complexity value–-was typically closest in mean squared error to the population factor pattern. We suggest that EFA researchers perform factor rotations from multiple starting points (e.g., 500 or more) with at least two rotation algorithms. Our results suggest that oblimin and oblique geomin rotations will identify simple structure configurations across many data scenarios. A full report of our findings is available in Nguyen and Waller (in press).