## Maximum Likelihood Estimation of Examinee Ability

Within the context of a test theory, a major goal is to obtain a measure of the ability of each examinee administered a educational test or psychological instrument. For a given examinee, this measure will be the maximum likelihood estimate of their unknown ability based upon their responses to the n items of the test and the values of the parameters of these items. In order to accomplish this estimation, three assumptions are made: First, the values of the parameters of the n dichotomously scored test items are known; Second, the examinees are independent objects and ability can be estimated on an examinee by examinee basis; Third, all n items in the test are modeled by ICC's of the same family. The maximum likelihood procedure for estimating an examinee's ability constitutes the second of the two basic building blocks of test analysis under IRT. While the overall logic of the maximum likelihood estimation of ability is the same under all ICC models, the mathematical details will differ as a function of the model. In the present chapter, these will be shown for the two-and three-parameter models.