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

摘要

Conditional P.D.F. Approach for estimating the operating characteristics of item response categories has been introduced earlier. In this study, a variation of this approach is introduced, which is called weighted sum procedure, in contrast to the previous one, which is now called simple sum procedure. The new method is applied to the same hypothetical data, i.e., the maximum likelihood estimates of ability of the five hundred hypothetical subjects and their responses to the ten binary items, each of which follows the normal ogive model. The criterion item characteristic function for each binary item is obtained and compared with the one obtained in the simple sum procedure to find out if the new procedure has possibilities for a better estimation than the previous one. This is actually done using 'pseudo' criterion item characteristic functions which adopt the approximated density functions of the maximum likelihood estimate by polynomials of degree 3, 4 and 5 by means of the method of moments. Also, the Pearson system method and the two-parameter beta method are used for both degree 3 and 4 cases in this variation of the conditional P.D.F. approach and the results are compared.