Title: Investigating differential options functioning using multinomial logistic regression

Authors: Minjeong Park; Amery D. Wu

Addresses: Department of ECPS, University of British Columbia Scarfe Building, 2125 Main Mall, Vancouver, BC V6T 1Z4, Canada ' Department of ECPS, University of British Columbia Scarfe Building, 2125 Main Mall, Vancouver, BC V6T 1Z4, Canada

Abstract: This paper focuses on an investigation of differential functioning in all options of multiple-choice items, referred to as differential options functioning (DOF). DOF is defined as an investigation into whether respondents from different groups (i.e. subpopulations), with equal levels of the attribute being measured (i.e. skill, ability, etc.) would have different probabilities to select the options. This paper aims to reconceptualise previous approaches to DOF in terms of its terminologies, purposes and uses. This paper further proposes a set of simple and integrated procedures for investigating DOF based on the well-known theory of multinomial logistic regression. A real data demonstration is provided to guide the application of the proposed method. The demonstration compares two test-language groups (English vs. French) on the four options of 15 multiple-choice items in booklet 13 of the 2011 Progress in International Reading Literacy Study.

Keywords: comprehensive differential item functioning; differential alternative analysis; differential distractor analysis; differential item functioning; differential options functioning; item responding; measurement bias; measurement invariance; multinomial logistic regression; multiple-choice question; option characteristic curves.

DOI: 10.1504/IJQRE.2017.086511

International Journal of Quantitative Research in Education, 2017 Vol.4 No.1/2, pp.94 - 119

Received: 05 Oct 2016
Accepted: 11 May 2017
Published online: 10 Sep 2017 *