Estimation of Ability

Abstract

Once an appropriate item response model is chosen, it is necessary to determine the values of the item and ability parameters that characterize each item and examinee. Since in the sequel we assume that the latent space is unidimensional, only one parameter, θ, characterizes an examinee. However, several parameters may characterize an item, and the number of item parameters is usually implied by the name of the item response model chosen. The item and ability parameters are usually unknown at some stage of model specification. Typically, a random sample (or calibration sample) from a target population is selected, and the responses to a set of items are obtained. Given the item responses, ability and item parameters are estimated. The item parameters estimated from the sample may be treated as known, and with this assumption item banks may be constructed. In subsequent applications, these items, which have known item parameter values, are administered to examinees and their abilities estimated. The basic problem is then that of determining the item and ability parameters from a knowledge of the responses of a group of examinees. In this chapter, we shall assume that item parameters are known from previous calibration and consider the problem of estimation of ability.