The Pearson and likelihood ratio statistics are frequently used for assessing the absolute fit of probability models. Researchers are often interested in comparing fits provided by different models which may have a subsuming or non-subsuming relation. A subsuming relation exists when the parameters of the reduced model form a subset of those contained in the subsuming, or full, model. A non-subsuming relation exists when the defining parameters in neither model form a subset of those defining the other model. A general "mixture" probability model which incorporates two non-subsuming probability models and a strategy for assessing fit provided by each of the component models is described. A detailed description of the strategy for selecting a preferred model is outlined. Applications of the suggested procedure are considered for the special case in which the Rasch latent trait model and Latent State Mastery model are compared as to relative preference when data are generated from each model. (DWH)