An empirical Bayesian approach to item banking

A procedure for the sequential optimization of the calibration of an item bank is given. The procedure is based on an empirical Bayesian approach to a reformulation of the Rasch model as a model for paired comparisons between the difficulties of test items in which ties are allowed to occur. First, it is shown how a paired-comparisons design deals with the usual incompleteness of calibration data and how the item parameters can be estimated using this design. Next, the procedure for a sequential optimization of the item parameter estimators is given, both for individuals responding to pairs of items and for item and examinee groups of any size. The paper concludes with a discussion of the choice of the first priors in the procedure and the problems involved in its generalization to other item response models.