In this commentary, University of North Carolina's associate dean of research and assessment at the School of Education Terry Ackerman poses questions and shares his thoughts on David Thissen's essay, "Bad Questions: An Essay Involving Item Response Theory" (this issue). Ackerman begins by considering the two purposes of Item Response…

Many latent traits in social sciences display a hierarchical structure, such as intelligence, cognitive ability, or personality. Usually a second-order factor is linearly related to a group of first-order factors (also called domain abilities in cognitive ability measures), and the first-order factors directly govern the actual item responses.…

Showed how Taylor approximation can be used to generate a linear approximation to a logistic item characteristic curve and a linear ability estimator. Demonstrated how, for a specific simulation, this could result in the special case of a Robbins-Monro item selection procedure for adaptive testing. (SLD)

A set of conditions is presented for the validity of inference for Item Response Theory (IRT) models applied to data collected from examinations that allow students to choose a subset of items. Common low-dimensional IRT models estimated by standard methods do not resolve the difficult problems posed by choice-based data. (SLD)

Some alternative criteria for item selection in adaptive testing are proposed that take into account uncertainty in the ability estimates. A simulation study shows that the likelihood weighted information criterion is a good alternative to the maximum information criterion. Another good alternative uses a Bayesian expected a posteriori estimator.…