Comparing item response theory models for ranking incorrect response options

TL;DR

This study evaluates the robustness of item response theory models, specifically the nominal response model, in ranking incorrect options in assessments without pre-specifying the correct answer, across multiple datasets.

Contribution

It extends previous work by applying the nominal response model to all response choices without assuming the correct answer, analyzing its consistency across diverse datasets.

Findings

Rankings without specifying the correct response are consistent in some datasets.

Noticeable differences in rankings occur across datasets.

Discrepancies may be due to response rate variations for less common options.

Abstract

Previous work has shown that item response theory may be used to rank incorrect response options to multiple-choice items on commonly used assessments. This work has shown that, when the correct response to each item is specified, a nominal response model (NRM) may be used to rank the incorrect options. We seek to determine the robustness of these results by applying the NRM to all response choices, without specifying the correct response. We apply these analyses to multiple data sets (each with more than 9,000 response sets), including pre-instruction and post-instruction responses. We find that the rankings generated without specifying the correct response are consistent with the previously published rankings for one data set; however, we find noticeable differences between rankings generated from different data sets. We provide evidence that discrepancies may result from differences in response rates for less commonly chosen responses.