  Computerized adaptive testing is becoming increasingly popular due to
advancement of modern computer technology. It differs from the conventional
standardized testing in that the selection of test items is tailored to
individual examinee's ability level. Arising from this selection strategy is a
nonlinear sequential design problem. We study, in this paper, the sequential
design problem in the context of the logistic item response theory models. We
show that the adaptive design obtained by maximizing the item information leads
to a consistent and asymptotically normal ability estimator in the case of the
Rasch model. Modifications to the maximum information approach are proposed for
the two- and three-parameter logistic models. Similar asymptotic properties are
established for the modified designs and the resulting estimator. Examples are
also given in the case of the two-parameter logistic model to show that without
such modifications, the maximum likelihood estimator of the ability parameter
may not be consistent.
