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 sug gested strategy are considered for the special case in which the Rasch item response model and a Latent State Mastery model are the component models com pared. Simulated data sets generated under each of these models were used to provide example applica tions of the proposed model selection strategy.