Item-Fit Statistic Based on Posterior Probabilities of Membership in Ability Groups

A novel approach to item-fit analysis based on an asymptotic test is proposed. The new test statistic, $$ , compares pseudo-observed and expected item mean scores over a set of ability bins. The item mean scores are computed as weighted means with weights based on test-takers' a posteriori density of ability within the bin. This article explores the properties of $$ in case of dichotomously scored items for unidimensional IRT models. Monte Carlo experiments were conducted to analyze the performance of $$ . Type I error of $$ was acceptably close to the nominal level and it had greater power than Orlando and Thissen's $$ . Under some conditions, power of $$ also exceeded the one reported for the computationally more demanding Stone's $$ .