Exploratory factor analysis with small sample sizes: a comparison of three approaches.

Exploratory factor analysis (EFA) has emerged in the field of animal behavior as a useful tool for determining and assessing latent behavioral constructs. Because the small sample size problem often occurs in this field, a traditional approach, unweighted least squares, has been considered the most feasible choice for EFA. Two new approaches were recently introduced in the statistical literature as viable alternatives to EFA when sample size is small: regularized exploratory factor analysis and generalized exploratory factor analysis. A simulation study is conducted to evaluate the relative performance of these three approaches in terms of factor recovery under various experimental conditions of sample size, degree of overdetermination, and level of communality. In this study, overdetermination and sample size are the meaningful conditions in differentiating the performance of the three approaches in factor recovery. Specifically, when there are a relatively large number of factors, regularized exploratory factor analysis tends to recover the correct factor structure better than the other two approaches. Conversely, when few factors are retained, unweighted least squares tends to recover the factor structure better. Finally, generalized exploratory factor analysis exhibits very poor performance in factor recovery compared to the other approaches. This tendency is particularly prominent as sample size increases. Thus, generalized exploratory factor analysis may not be a good alternative to EFA. Regularized exploratory factor analysis is recommended over unweighted least squares unless small expected number of factors is ensured.