A large sample method for obtaining asymptotic simultaneous confidence bands for a three-parameter logistic response curve is described. Simultaneous confidence bands indicate the sampling variation of item response curves relative to a fitted function. A procedure is given which requires as input maximum likelihood parameter estimates and an…

Formulas are derived for the bias in the maximum likelihood estimators (MLE) of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission. Most typically the bias of an MLE is about one-tenth of its standard error. It is very seldom more…

A possible method is developed 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 and with the variance-covariance matrices found by the usual…

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;…

Explored are two theoretical approaches that attempt to cope with omitted responses, that is, when an examinee omits (fails to respond to) an item and therefore the item response formula cannot be used. Preliminary considerations are discussed, and it is shown that a conveniently simple application of equivalent items leads to internal…

There are currently three main approaches to parameter estimation in item response theory (IRT): (1) joint maximum likelihood, exemplified by LOGIST, yielding maximum likelihood estimates; (2) marginal maximum likelihood, exemplified by BILOG, yielding maximum likelihood estimates of item parameters (ability parameters can be estimated…

Given known item parameters for a test, unbiased estimators are derived for an examinee's ability parameter, his or her proportion correct true score for the variances of these parameters and for the parallel forms reliability of the maximum likelihood estimator of the ability parameter. (Author/JKS)

Asymptotic formulas are derived for the bias in the maximum likelihood estimators of the item parameters in the logistic item response model when examinee abilities are known. Numerical results are given for a typical verbal test for college admission. (Author)

Advantages and disadvantages of joint maximum likelihood, marginal maximum likelihood, and Bayesian methods of parameter estimation in item response theory are discussed and compared. (Author)

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…