SEM Estimation in the Context of Small Samples: Comparison of Latent Variable Models, Single Indicator, Regularized2-Stage Least Squares and Observed Variable Models

Abstract

Structural Equation Models (SEMs) are widely used in the social sciences. These models explicitly model statistical error, thereby yielding more accurate and efficient parameter estimates than do observed variable methods such as regression. However, SEM requires larger samples in order to work properly. Therefore, researchers working with small samples are faced with the choice of appropriately modeling measurement error with too few cases, or inappropriately ignoring it with a method that better accommodates smaller samples. To address this problem, alternatives have been developed, including the single indicator approach using reliability to set error variances for composite indicator variables, and regularized 2-stage least squares. This study compares these methods with one another, factor score regression, SEM, and observed variable models. Results revealed that the performance of the methods depended upon the underlying model being fit, as well as sample size and population reliability. Implications for practice are provided in the discussion.