In item-response theory, if a latent-structure model has an ability variable, then elementary information theory may be employed to provide a criterion for evaluation of the information the test provides concerning ability. This criterion may be considered even in cases in which the latent-structure model is not valid, although interpretation of…

The purpose of this article is to reflect on the state of the theorizing and praxis of DIF in general: where it has been; where it is now; and where I think it is, and should, be going. Along the way the major trends in the differential item functioning (DIF) literature are summarized and integrated providing some organizing principles that allow…

Adaptive quadrature is applied to marginal maximum likelihood estimation for item response models with normal ability distributions. Even in one dimension, significant gains in speed and accuracy of computation may be achieved.

Latent-class item response models with small numbers of latent classes are quite competitive in terms of model fit to corresponding item-response models, at least for one- and two-parameter logistic (1PL and 2PL) models. Provided that care is taken in terms of computational procedures and in terms of use of only limited numbers of latent classes,…