AIC-type Theory-Based Model Selection for Structural Equation Models

Structural equation modeling (SEM) software commonly report information criteria, like the AIC, for the model under investigation and for the unconstrained/saturated model. With these criteria, (non-)nested models can be compared. This comes down to evaluating equalities (e.g., setting some paths equal or to 0). These criteria cannot evaluate inequality restrictions on the parameters, while the AIC-type criterion called GORICA can. For example, GORICA can evaluate the hypothesis stating that one predictor has more (standardized) strength than some other predictors. This paper illustrates inequality-constrained hypothesis-evaluation in SEM models using the GORICA (in R). Examples will be presented for confirmatory factor analysis, latent regression, and multigroup latent regression.