Model Close Match as a Criterion for Structured Model Comparison and Its Robust Statistical Tests (June 2008 Revision)

Traditional model comparison procedure selects nested structured models by evaluating the feasibility of the equality constraints that differentiate the models. We propose instead to evaluate model close match, using the distance between two models, either as important supplementary information or as a criterion for nested model comparison. Based on MacCallum, Browne and Cai (2006) and the results of Vuong (1989) and Yuan, Hayashi and Bentler (2007), we develop a reasonable cutoff value and some ADF-like tests for inference on model closeness. Simulation studies show that several of our proposed tests have robust and desirable performance in spite of severe nonnormality when sample size is as large as 150. Consequently, a two-stage procedure which combines the traditional nested model comparison and the additional inferential information regarding model close match is further suggested to improve the typical practice of model modification