Estimation of the Operating Characteristics of Item Response Categories. VIII. Bivariate P.D.F. Approach with Normal Approach Method.
TENNESSEE UNIV KNOXVILLE DEPT OF PSYCHOLOGY
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Bivariate P.D.F. Approach for estimating the operating characteristics of item response categories is introduced, and used in conjunction with the Normal Approach Method, assuming a normal distribution for the conditional distribution of ability, given its maximum likelihood estimate. In this approach, the total set of the maximum likelihood estimates is divided into the item score groups, and for each score group the density function of the maximum likelihood estimate is approximated by a polynomial. It is tried on 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 following the normal ogive model. Three different degrees of polynomials are used in approximating the density functions of the subsets of the maximum likelihood estimates, and they are called Degree 3, 4 and 5 Cases. The mean square errors are used for evaluating the resultant estimated item characteristic functions, and the two item parameters in the normal ogive model are also estimated.
- Statistics and Probability