An Alternative Estimator for the Maximum Likelihood Estimator for the Two Extreme Response Patterns

摘要

In the methods and approaches we have developed for estimating the operating chracteristics of the discrete item responses, the maximum likelihood estimate of the examinee based upon the 'Old Test' has an important role. When Old Test does not provide us with a sufficient amount of test information for the upper and lower part of the ability interval, however, it is likely that we obtain response patterns which are either all lowest item scores or all highest item scores, and the resultant maximum likelihood estimates are negative or positive infinity. Although such a test is undesirable for us to use as the Old Test, to a certain extent we can salvage the situation by providing some alternative estimator for these two extreme response patterns. Following RR-80-3, 'Is Bayesian Estimation Proper for Estimating the Individual's Ability', in the present paper, such an estimator is proposed and discussed. (Author)