Local Minima and Factor Rotations in Exploratory Factor Analysis

In exploratory factor analysis, factor rotation algorithms can converge to local solutions (i.e., local minima) when they are initiated from different starting points. To better understand this problem, we performed three studies that investigated the prevalence and correlates of local solutions with five factor rotation algorithms: varimax, oblimin, entropy, and geomin (orthogonal and oblique). 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) factor loading standardization, (f) sample size, and (g) model approximation error on the frequency of local solutions in factor rotation. We also examined local solutions in an exploratory factor analysis of an open source data set that included 54 personality items. Across three studies, all five algorithms converged to local solutions under some conditions with geomin (orthogonal and oblique) producing the highest number of local solutions. Follow-up analyses showed that, when factor rotations produced multiple solutions, the factor pattern with the maximum hyperplane count (rather than the lowest complexity value) was typically closest in mean squared error to the population factor pattern. Translational Abstract In exploratory factor analysis, factor rotation algorithms can converge to local solutions (i.e., local minima) when they are initiated from different starting points. To better understand this problem, we performed three studies that investigated the prevalence and correlates of local solutions with five factor rotation algorithms: varimax, oblimin, entropy, and geomin (orthogonal and oblique). 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) factor loading standardization, (f) sample size, and (g) model approximation error on the frequency of local solutions in factor rotation. We also examined local solutions in an exploratory factor analysis of an open source data set that included 54 personality items. Across three studies, all five algorithms converged to local solutions under some conditions with geomin (orthogonal and oblique) producing the highest number of local solutions. Follow-up analyses showed that, when factor rotatio