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.