Investigating differential options functioning using multinomial logistic regression

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.