A new item response theory model to adjust data allowing examinee choice

In a typical questionnaire testing situation, examinees are not allowed to choose which items they answer because of a technical issue in obtaining satisfactory statistical estimates of examinee ability and item difficulty. This paper introduces a new item response theory (IRT) model that incorporates information from a novel representation of questionnaire data using network analysis. Three scenarios in which examinees select a subset of items were simulated. In the first scenario, the assumptions required to apply the standard Rasch model are met, thus establishing a reference for parameter accuracy. The second and third scenarios include five increasing levels of violating those assumptions. The results show substantial improvements over the standard model in item parameter recovery. Furthermore, the accuracy was closer to the reference in almost every evaluated scenario. To the best of our knowledge, this is the first proposal to obtain satisfactory IRT statistical estimates in the last two scenarios.