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A Hierarchical Model for Accuracy and Choice on Standardized Tests

Published online by Cambridge University Press:  01 January 2025

Steven Andrew Culpepper and
James Joseph Balamuta
Steven Andrew Culpepper*
Affiliation:
University of Illinois at Urbana-Champaign
James Joseph Balamuta
Affiliation:
University of Illinois at Urbana-Champaign
*
Correspondence should be made to Steven Andrew Culpepper, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL 61820, USA. Email: sculpepp@illinois.edu, balamut2@illinois.edu
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Abstract

This paper assesses the psychometric value of allowing test-takers choice in standardized testing. New theoretical results examine the conditions where allowing choice improves score precision. A hierarchical framework is presented for jointly modeling the accuracy of cognitive responses and item choices. The statistical methodology is disseminated in the ‘cIRT’ R package. An ‘answer two, choose one’ (A2C1) test administration design is introduced to avoid challenges associated with nonignorable missing data. Experimental results suggest that the A2C1 design and payout structure encouraged subjects to choose items consistent with their cognitive trait levels. Substantively, the experimental data suggest that item choices yielded comparable information and discrimination ability as cognitive items. Given there are no clear guidelines for writing more or less discriminating items, one practical implication is that choice can serve as a mechanism to improve score precision.

Keywords

high-stakes testingitem response theoryThurstonian modelsBayesian statisticschoice

Information

Type
Original paper
Information
Psychometrika , Volume 82 , Issue 3 , September 2017, pp. 820 - 845
Copyright
Copyright © 2015 The Psychometric Society

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