## Estimating the Parameters of an Item Characteristic Curve

One of the salient characteristics of item response theory is that the major constructs of the theory are based upon items and the parameters of a model for the item characteristic curve. In the previous chapter, the several models for dichotomously scored items and their parameterization were introduced. Given the responses of examinees to the items of a test, the task is then to characterize the items via the numerical values of the item parameters. To accomplish this, a selected item characteristic curve model must be fitted to the response data for each item in a test. While the parameters of the items in a test could be estimated sitnultaneously, this leads to computationally demanding procedures that are not economically feasible. Thus, in most of the IRT test analysis procedures the item parameters are estimated on a one item at a time basis. Because of this, a technique for estimating the parameters of a single item is one of the two basic building blocks of test analysis under IRT. In the present chapter, it will be assumed that the ability scores of the examinees responding to a test item are known. This assumption greatly simplifies the estimation process and it is employed in most of the approaches to be discussed in later chapters. In addition, it places the estimation procedures within the context of the well known statistical techniques for quantal-response bioassay.