A Comparison of Regularized Maximum-Likelihood, Regularized 2-Stage Least Squares, and Maximum-Likelihood Estimation with Misspecified Models, Small Samples, and Weak Factor Structure

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Several structural equation modeling estimation methods have recently been developed to alleviate problems associated with model misspecification. Two of the more popular such approaches are 2-stage least squares and regularization methods. Prior work examining the performance of these estimators has generally focused on problems with adequately sized samples and relatively large factor loadings. In contrast, relatively little research has been conducted comparing these estimation techniques with small samples and weak loadings, though both conditions are not uncommon in the multivariate modeling. The current simulation study focused on comparing these relatively new structural estimation methods for misspecified models (e.g., misspecified interactions and cross-loadings) with small samples and relatively weak factor loadings. Results indicated that regularized 2-stage least squares estimation performed better compared to the regularized structural equation modeling framework for small samples and with weak factor loadings. Implications and guidelines for applied researchers are presented.