Parameters

This paper seeks to extend the application of Markov chain Monte Carlo (MCMC) methods in item response theory (IRT) to include the estimation of equating relationships along with the estimation of test item parameters. A method is proposed that incorporates estimation of the equating relationship in the item calibration phase. Item parameters from a previous calibration of one test form are used to construct informative prior distributions to be used in the new simultaneous calibration of the two test forms. Data were from the standardization of the Comprehensive Test of Basic Skills, Fifth Edition for an eighth-grade mathematics test, with 3,171 examinees used to obtain initial estimates for the anchor test (set A) parameters, 2,000 examinees in the equating process, and 4,000 examinees used to evaluate the effectiveness of the various methods. The new method was compared to traditional methods based on marginal maximum likelihood calibration followed by a Stocking and Lord (M. Stocking and F. Lord, 1983) linear transformation. Results indicate that the new approach can lead to modest improvement in equating accuracy. Under this approach, the predicted scores for a validation group have higher correlations and lower root mean square errors in comparison to observed scores. (SLD) Reproductions supplied by EDRS are the best that can be made from the ori inal document