Regularized Exploratory Bifactor Analysis With Small Sample Sizes

Several methods of factor extraction have recently gained popularity as a procedure for dealing with estimation problems associated with small sample sizes, which can be found in the various behavioral science disciplines, such as comparative psychology and behavior genetics. Two popular approaches for particularly small samples (below 50) include unweighted least squares factor analysis (ULS-FA) and regularized exploratory factor analysis (REFA). However, it is unclear how well each of the approaches performs with small samples in the context of exploratory bifactor modeling. In the current study, a comprehensive simulation study was conducted to evaluate the small sample behavior of the two approaches in terms of bifactor structure recovery under different sample size, factor loading, number of variables per factor, number of factors, and factor correlation experimental conditions. The results show that REFA is recommended for use over ULS-FA, particularly in the conditions involving low factor loadings, few group factors, or a small number of variables per factor.