A framework of facets item response theory models

The Rasch facets model has been developed to account for facets data, such as students’ responses to essays are graded by raters. In the facets model, ratings given to essays are treated as “virtual” items. In theory, the difficulties of these virtual items can be decomposed into a main effect of actual essays, a main effect of raters, and an interaction effect of essay by rater. To achieve better measurement quality, in the facets model, the interaction effect is constrained at zero (i.e., a rater’s severity is constant across essay items). Just like the slope parameters can be added to the simple Rasch model to form the two-parameter model, so too for the Rasch facets model. Furthermore, similar to the linear decomposition on the item difficulties of virtual items, the slope parameters of the virtual items can be decomposed into main and interaction effects. A new framework for facets model is thus developed by setting a series of constrains on the main and interaction effects. The simulation results show that the parameters of the new class of facets models could be well recovered. Three empirical examples were provided. Further model generation is discussed.