Selecting Path Models in SEM: A Comparison of Model Selection Criteria

Model comparison is one useful approach in applications of structural equation modeling. Akaike’s information criterion (AIC) and the Bayesian information criterion (BIC) are commonly used for selecting an optimal model from the alternatives. We conducted a comprehensive evaluation of various model selection criteria, including AIC, BIC, and their extensions, in selecting an optimal path model under a wide range of conditions over different compositions of candidate set, distinct values of misspecified parameters, and diverse sample sizes. The chance of selecting an optimal model rose as the values of misspecified parameters and sample sizes increased. The relative performance of AIC and BIC type criteria depended on the magnitudes of the parameter misspecified. The BIC family in general outperformed AIC counterparts unless under small values of omitted parameters and sample sizes, where AIC performed better. Scaled unit information prior BIC (SPBIC) and Haughton's BIC (HBIC) demonstrated the highest accuracy ratios across most of the conditions investigated in this simulation.