An application of a hierarchical IRT model for items in families generated through the application of different combinations of design rules is discussed. Within the families, the items are assumed to differ only in surface features. The parameters of the model are estimated in a Bayesian framework, using a data-augmented Gibbs sampler. An obvious…

Current modeling of response times on test items has been strongly influenced by the paradigm of experimental reaction-time research in psychology. For instance, some of the models have a parameter structure that was chosen to represent a speed-accuracy tradeoff, while others equate speed directly with response time. Also, several response-time…

Dichotomous item response theory (IRT) models can be viewed as families of stochastically ordered distributions of responses to test items. This paper explores several properties of such distributions, especially those related to transfer to other distributions. Results are formulated as a series of theorems and corollaries that apply to…

A maximin model for test design based on item response theory is proposed. Only the relative shape of target test information function is specified. It serves as a constraint subject to which a linear programing algorithm maximizes the test information. The model is illustrated, and alternative models are discussed. (TJH)

Derives a set of linear conditions of item-response functions that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly. An example illustrates the use of the model for an item pool from the Law School Admissions Test (LSAT). (SLD)