Optimal ranking of test items using the Rasch model

Divyanshu Vats, Andrew S. Lan, Christoph Studer, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the problem of ranking test items, i.e., the ordering of items according to the amount of information they provide on the latent trait of the respondents. We focus on educational applications, where instructors are interested in ranking questions so as to select a small set of informative questions in order to efficiently assess the students' understanding on the course material. Using the Rasch model for modeling student responses, we prove that the simple algorithm of sorting the item level parameters of the Rasch model is optimal in the setting where the goal is to maximize the entropy of the student responses. We demonstrate the optimality of the sorting algorithm using both theoretical results and using empirical results on several real-world datasets. Furthermore, we also demonstrate how the sorting algorithm can be used in a batch adaptive manner for predicting unobserved student responses.

Original languageEnglish (US)
Title of host publication54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages467-473
Number of pages7
ISBN (Electronic)9781509045495
DOIs
StatePublished - Feb 10 2017
Event54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016 - Monticello, United States
Duration: Sep 27 2016Sep 30 2016

Other

Other54th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2016
CountryUnited States
CityMonticello
Period9/27/169/30/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Computational Theory and Mathematics
  • Computer Networks and Communications
  • Hardware and Architecture
  • Control and Optimization

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