ESTIMATION OF ITEM RESPONSE THEORY MODELS WHEN ABILITY IS UNIFORMLY DISTRIBUTED

Abstract

Item Response Theory (IRT) models traditionally assume a normal distribution for ability. Although normality is often a reasonable assumption for ability, it is rarely met for observed scores in educational and psychological measurement. Assumptions regarding ability distribution were previously shown to have an effect on IRT parameter estimation. In this study, the normal and uniform distribution assumptions for ability were compared for IRT parameter estimation, when the actual distribution was either normal or uniform. Uniform distribution assumption in 2PL model yielded more accurate estimates of ability independent of the actual ability distribution. Similarly, a uniform distribution assumption for ability yielded more accurate estimates of ability in 3PL model when the actual ability distribution was uniform. For Rasch model, there was not an explicit pattern for comparing accuracy of ability estimates from uniform and normal distribution assumptions.