BIC and Alternative Bayesian Information Criteria in the Selection of Structural Equation Models.

Selecting between competing Structural Equation Models (SEMs) is a common problem. Often selection is based on the chi square test statistic or other fit indices. In other areas of statistical research Bayesian information criteria are commonly used, but they are less frequently used with SEMs compared to other fit indices. This article examines several new and old Information Criteria (IC) that approximate Bayes Factors. We compare these IC measures to common fit indices in a simulation that includes the true and false models. In moderate to large samples, the IC measures outperform the fit indices. In a second simulation we only consider the IC measures and do not include the true model. In moderate to large samples the IC measures favor approximate models that only differ from the true model by having extra parameters. Overall, SPBIC, a new IC measure, performs well relative to the other IC measures.