Random Item MIRID Modeling and Its Application

The Model With Internal Restrictions on Item Difficulty (MIRID; Butter, 1994) has been useful for investigating cognitive behavior in terms of the processes that lead to that behavior. The main objective of the MIRID model is to enable one to test how component processes influence the complex cognitive behavior in terms of the item parameters. The original MIRID model is, indeed, a fairly restricted model for a number of reasons. One of these restrictions is that the model treats items as fixed and does not fit measurement contexts where the concept of the random items is needed. In this article, random item approaches to the MIRID model are proposed, and both simulation and empirical studies to test and illustrate the random item MIRID models are conducted. The simulation and empirical studies show that the random item MIRID models provide more accurate estimates when substantial random errors exist, and thus these models may be more beneficial.