Estimation of the Operating Characteristics of Item Response Categories. VI. Proportioned Sum Procedure in the Conditional P.D.F. Approach.

摘要

Following Simple Sum Procedure and Weighted Sum Procedure, another method, Proportioned Sum Procedure, is introduced in the context of the Conditional P.D.F. Approach. The new method is somewhat different from the previous two, however, in the sense that the set of conditional density functions is not exclusively recategorized into the item score groups, but they are proportioned into each item score category. The same hypothetical data, i.e., the maximum likelihood estimates of the five hundred hypothetical subjects and their responses to the ten binary items, each of which follows the normal ogive model, are used to try the method. The criterion item characteristic function for each binary item is obtained and compared with those obtained by the other two procedures. The Pearson System Method and the Two-Parameter Beta Method are used for both Degree 3 and 4 Cases, and the results are compared with the previous ones. The mean square errors are adopted in evaluating both the resultant estimated item characteristic functions and probability density functions of ability. The two item parameters in the normal ogive model are also estimated for each item, and the results are compared with the previous ones. (Author)