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), a large sample Model Selection 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 nonnested 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. Copyright 2000 Academic Press.