The Uniform Prior for Bayesian Estimation of Ability in Item Response Theory Models

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 prior assumptions for ability were compared for IRT parameter estimation when the actual distribution was either normal or uniform. A simulation study that included a short test with a small sample size and a long test with a large sample size was conducted for this purpose. The results suggested using a uniform distribution prior for ability to achieve more accurate estimates of the ability parameter in the 2PL and 3PL models when the true distribution of ability is not known. For the Rasch model, an explicit pattern that could be used to obtain more accurate item parameter estimates was not found.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 prior assumptions for ability were compared for IRT parameter estimation when the actual distribution was either normal or uniform. A simulation study that included a short test with a small sample size and a long test with a large sample size was conducted for this purpose. The results suggested using a uniform distribution prior for ability to achieve more accurate estimates of the ability parameter in the 2PL and 3PL models when the true distribution of ability is not known. For the Rasch model, an explicit pattern that could be used to obtain more accurate item parameter estimates was not found.