Performance of Information Complexity Criteria in Structural Equation Models with Applications

A common problem in structural equation modeling is that of model selection. Many researchers have addressed this problem, but many methods have provided mixed benefits until recently. Akaike's well-known criteria, AIC, has been applied in the context of structural equation modeling, but the effectiveness of many other information criteria have not been studied in a convincing manner. In this paper, we compare the SEM model selection prowess of several AIC-type and ICOMP-type criteria. We also introduce two new large sample consistent forms of Bozdogan's ICOMP criteria - one of which is robust to model misspecification. To study the empirical performance of the information criteria, we use a well-known SEM simulation protocol, and demonstrate that most of the information-theoretic criteria select the "pseudo true" model with very high frequencies. We also demonstrate, however, that the performance of AIC is inversely related to the sample size. Finally, we apply the new criteria to select an analytical model for a real dataset from a retail marketing study of consumer behavior. Our results show the versatility of the new proposed method where both the goodness-of fit and the complexity of the model is taken into account in one criterion function.