Methodology review: Item parameter estimation under the one-, two-, and three-parameter logistic models

Abstract

This paper surveys the techniques used in item response theory to estimate the parameters of the item characteristic curves fitted to item response data. The major focus is on the joint maximum likelihood estimation (JMLE) procedure, but alternative approaches are also examined. The literature shows that both the theoretical asymptotic properties and the empirical properties of the JMLE results are well-established. Although alternative approaches are available, such as Bayesian estimation and marginal maximum likelihood estimation, they do not appear to have an overwhelming advantage over the JMLE procedure. However, the properties of these alternative techniques have not been thoroughly studied as yet. It is also clear that the properties of the item parameter estimation techniques are inextricably intertwined with the computer programs used to implement them.