一般項目反応モデルにおける項目パラメタの周辺最尤推定法

Abstract

According to the Thurstonean point of view, a usual two-parameter normal ogive model can be derived as a special case of the Law of Categorical Judgement, where all subjects have common dispersion parameter. The generalized item response (GIRT) model, first proposed by Torgerson (1958), is an extension of the IRT model, in which each subject is characterized not only by the ability parameter (θ) but also by the dispersion parameter (Φ). For a subject characterized by (θ, Φ), the probability that he/she answers the item correctly is given by Pr (U=1|θ, Φ) =φ ((θ-b)), where φ is the standard normal or logistic distribution function and (a, b) constitutes the set of usual item parameters. In this article, an item parameter estimation method maximizing the marginal likelihood where the subject parameters (θ, Φ) are integrated out, is presented.