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Abstract
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.
Highlights
Item response theory (IRT) comprises a set of statistical models for measuring examinee abilities through their answers to a set of items
The results show substantial improvements in the accuracy of the estimated parameters compared to the standard Rasch model, mainly in situations in which examinee choice is different from a random selection of items
This paper proposes a new IRT model that takes into account the relation shown in Eq 18
Summary
Item response theory (IRT) comprises a set of statistical models for measuring examinee abilities through their answers to a set of items (questionnaire). One of the most important advantages of IRT is allowing comparison between examinees who answered different tests This property, known as invariance, is obtained by introducing separate parameters for the examinee abilities and item difficulties [1]. If the examinees are allowed to choose a subset of items, instead of answering them all, the model estimates may become seriously biased. This problem has been raised by many researchers [2,3,4,5,6,7,8] but still lacks a satisfactory solution
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