Mixture Rasch Models With Joint Maximum Likelihood Estimation

Abstract

This research provides a demonstration of the utility of mixture Rasch models. Specifically, a model capable of estimating a mixture partial credit model using joint maximum likelihood is presented. Like the partial credit model, the mixture partial credit model has the beneficial feature of being appropriate for analysis of assessment data containing any combination of dichotomous and polytomous item types. Mixture Rasch models are able to provide information regarding latent classes (subpopulations without manifest grouping variables) and separate item parameter estimates for each of these latent classes. In this research, the step parameters were constrained to be equal across items, making the model a mixture rating scale model. An analysis with simulated data provides a clear example demonstration followed by a real-world analysis and interpretation of student survey data.