  In computerized adaptive testing (CAT), items (questions) are selected in
real time based on the already observed responses, so that the ability of the
examinee can be estimated as accurately as possible. This is typically
formulated as a non-linear, sequential, experimental design problem with binary
observations that correspond to the true or false responses. However, most
items in practice are multiple-choice and dichotomous models do not make full
use of the available data. Moreover, CAT has been heavily criticized for not
allowing test-takers to review and revise their answers. In this work, we
propose a novel CAT design that is based on the polytomous nominal response
model and in which test-takers are allowed to revise their responses at any
time during the test. We show that as the number of administered items goes to
infinity, the proposed estimator is (i) strongly consistent for any item
selection and revision strategy and (ii) asymptotically normal when the items
are selected to maximize the Fisher information at the current ability estimate
and the number of revisions is smaller than the number of items. We also
present the findings of a simulation study that supports our asymptotic
results.
