SAMPLING VARIANCES AND COVARIANCES OF PARAMETER ESTIMATES IN ITEM RESPONSE THEORY

Abstract

ABSTRACT This paper develops a possible method for computing the asymptotic sampling variance‐covariance matrix of joint maximum likelihood estimates in item response theory when both item parameters and abilities are unknown. For a set of artificial data, results are compared with empirical values; also with the variance‐covariance matrices found by the usual formulas for the case where the abilities are known, or where the item parameters are known. The results are consistent with the conjecture that the new method is asymptotically correct except for errors due to grouping.