Estimation of the Operating Characteristics of Item Response Categories IV: Comparison of the Different Methods.

摘要

The three methods of estimating the operating characteristics of item response categories have been developed and tried on a set of simulated data, in which five hundred hypothetical examinees are assumed and their responses to test items are calibrated by the Monte Carlo method. They are Two-Parameter Beta Method, Normal Approach Method and Pearson System Method. There have been introduced three different categories of methods, i.e., Histogram Ratio Method, Curve Fitting Method and Conditional P.D.F. Method, and they have been tried, Mainly, within the context of the Two-Parameter Beta Method. In the present paper, all the findings are summarized and pursued further, in the attempt of reaching a tentative conclusion, with the awareness that we need more varieties of different types of data to fully understand and appreciate each method and technique. Throughout these studies, a polynomial of degree 3 or of degree 4 is used to approximate the marginal density function of the maximum likelihood estimate, to distinguish Degree 3 and 4 Cases from each other. Comparison is also made in an attempt to find out whether Degree 4 Case, which obviously has a theoretical advantage over Degree 3 Case, provides as with substantial gain in the accuracy of operating characteristic estimation. (Author)