  Item response theory (IRT) models have been widely used in educational
measurement testing. When there are repeated observations available for
individuals through time, a dynamic structure for the latent trait of ability
needs to be incorporated into the model, to accommodate changes in ability.
Other complications that often arise in such settings include a violation of
the common assumption that test results are conditionally independent, given
ability and item difficulty, and that test item difficulties may be partially
specified, but subject to uncertainty. Focusing on time series dichotomous
response data, a new class of state space models, called Dynamic Item Response
(DIR) models, is proposed. The models can be applied either retrospectively to
the full data or on-line, in cases where real-time prediction is needed. The
models are studied through simulated examples and applied to a large collection
of reading test data obtained from MetaMetrics, Inc.

Applications