Golden, R. M. (in press). Statistical tests for comparing possibly misspecified and non-nested models. Journal of Mathematical Psychology, ??, ??-???.
Model Selection Criteria (MSC) involves selecting the model with the best "estimated goodness-of-fit" to the data generating process. Following the method of Vuong (1989, {\em Econometrica, 57}, 307-333), a large sample Model Selection Statistical Test (MST) is introduced that can be used in conjunction with most existing MSC procedures to decide if the estimated goodness-of-fit for one model is significantly different from the estimated goodness-of-fit for another model. The MST extends the classical generalized likelihood ratio test, is valid in the presence of model misspecification, and is applicable to situations involving non-nested probability models. Simulation studies designed to illustrate the concept of the MST and its conservative decision rule (relative to the MSC method) are also presented.