Estimation of the Operating Characteristics of Item Response Categories II: Further Development of the Two-Parameter Beta Method.
TENNESSEE UNIV KNOXVILLE DEPT OF PSYCHOLOGY
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The Two-Parameter Beta Method, introduced in the previous study as a method of estimating the operating characteristics of a test item, has proved to be as efficient as the Normal Approximation Method, for a set of simulated data of 500 hypothetical examinees having a uniform latent trait distribution between -2.475 and 2.475. Both methods are characterized 1 by the use of a relatively small number of subjects-like 500 -- in the whole procedure of estimation 2 without assuming any prior mathematical model and 3 by the use of the estimated joint distribution of the latent trait and its maximum likelihood estimate. In the Two-Parameter Beta Method, the method of moments is adopted to approximate the probability density function of the maximum likelihood estimate, using polynomials of degree 3 and 4. The first two conditional moments of the latent trait, given the maximum likelihood estimate, are derived from theory and computed for the data for each value of the maximum likelihood estimate. The conditional distribution of the latent trait, given the maximum likelihood estimate, is approximated by a Beta distribution using the method of moments, with two a priori set parameters and two estimated parameters from the conditional moments.
- Statistics and Probability