This paper is primarily concerned with determining the statistical bias in the maximum likelihood estimate of the examinee ability parameter in item response theory, and of certain functions of such parameters. Given known item parameters, unbiased estimators are derived for (1) an examinee's ability parameter and proportion-correct true score;…

The EM algorithm is used to derive maximum likelihood estimates for item parameters of the two-parameter logistic item response curves. The observed information matrix is then used to approximate the covariance matrix of these estimates. Simulated data are used to compare the estimated and actual item parameters. (Author/BW)

The sampling errors of maximum likelihood estimates of item-response theory parameters are studied in the case where both people and item parameters are estimated simultaneously. A check on the validity of the standard error formulas is carried out. The effect of varying sample size, test length, and the shape of the ability distribution is…