Bayesian Marginal Joint Models for Responses and Process Data (PR 18-03)

With computerized testing, it is possible to record not only the responses of test takers to test questions but also other details about the test taker’s activity, such as the amount of time spent responding to each question. These details comprise a new type of data called process data. This report proposes a new approach to modeling responses, response times, and other process data: Test-taker data that naturally belong together are grouped in a cross-classification structure. Five examples of models applying this approach are illustrated. This new approach was evaluated in a simulation study and compared to the classical approach. A model that allows for variations in test-taker speed and accuracy produced satisfactory results. This model also lent insight into changes in the speed–accuracy trade-off over the course of the test.