Estimation of Ability Using Pseudocounts in Item Response Theory

Abstract

A method for estimation of ability using pseudocounts in dichotomous item response models is given when associated item parameters are known or estimated by a separate calibration sample of examinees with the size of an appropriate order. The pseudocount minimizing the asymptotic mean square error is algebraically obtained. Though the pseudocount depends on unknown ability, a fixed lower bound for the pseudocount is derived under the logistic model with equivalent items. The lower bound is numerically shown to be reasonable under the 3-parameter logistic model with and without model misspecification.