Chapter 8: Mixture Models in A Developmental Context

Mixture item response theory (IRT) models are based on the assumption that the population being measured is composed of two or more latent subpopulations, each of which responds to a set of tasks in predictably different ways. Within each subpopulation, a latent trait model holds for the entire set of tasks; however, between the subpopulations, there are differences that cannot be described within the constraints of the latent trait model used for a given subpopulation.

One of the most general mixture IRT models is the mixed Rasch model (Rost, 1990). This model assumes that the population in question is made up of H subpopulations, and that a Rasch model holds within each subpopulation. There is no necessary relation among the various Rasch models; the ordering of the items in terms of their difficulty can be entirely different for each subpopulation. This model is exploratory in the sense that it simply divides the population into the “best” (i.e., most different) set of subpopulations. The user must then determine what is interesting about the differences among subpopulations.