A Probit Multistate IRT Model With Latent Item Effect Variables for Graded Responses

Abstract: A probit multistate Item Response Theory (IRT) model for ordinal response variables is introduced. It comprises a reference latent state variable for each occasion of measurement and a latent item effect variable for each item except for one reference item. The latent item effect variable is defined as the difference between the latent state variable pertaining to the non-reference item and the latent state variable pertaining to the reference item. They are assumed to be identical for all occasions of measurement. The new model is applied to a real data example. Including item effect variables improve model fit considerably. Hence, the items are not strictly unidimensional within each occasion of measurement.