Comparing fit of nonsubsuming probability models

Abstract

A "mixture" probability model that incorporates two component models defined by nonsubsuming sets of parameters is introduced, and a strategy for using this model in the selection of a preferred component model is developed. Example applications of the suggested strategy are considered for the special case in which the Rasch item response model and a Latent State Mastery model are the component models compared. Simulated data sets generated under each of these models were used to provide example applications of the proposed model selection strategy.