ITEM RESPONSE THEORY USING A FINITE MIXTURE OF LOGISTIC MODELS WITH ITEM-SPECIFIC MIXING WEIGHTS

Abstract

Since a latent trait θ can not be directly observed in item response theory models, it is difficult to specify an item response function (IRF). Many mathematical models have been proposed, among which the two-parameter logistic model (2PLM) is often included. In this article, we will propose a new parametric model, namely, a finite mixture of logistic models (MLM). The MLM has different mixing weights per item, and can model a plateau in the learning curve, which is a well-known phenomenon in education and psychology. It is also known that finite mixtures have some problems with estimating item parameters. Therefore, we develop a new useful estimation algorithm for item parameters and present simulation studies which show that this estimation algorithm works well. In fact, when the MLM was applied to analyze real data, we also found that the MLM makes it possible to distinguish whether or not a plateau appears in an IRF, whereas the 2PLM does not have this capability.