Application of two-parameter Nested Logit model in identifying the source of DIF in multiple-choice items.

Identifying distractors as sources of Differential Item Functioning(DIF) in polytomous items has great importance to designers and analysts. Although DIF is one of the common methods for examining the measurement invariance, It is accompanied by challenges and limitations, especially in multiple-choice items. The purpose of this study was to assess the performance of the Nested logit Model(NLM) for detecting Differential Distractor Functioning(DDF) by using experimental (simulated data) and descriptive-analytical (real data) methods. Six items were simulated under different conditions of difficulty and slope, ability distribution, presence or absence of DIF/DDF, and DIF/DDF magnitude, with a sample size of 2000 and 50 replicates. The data of the Math Entrance Exam (D-form,2018), with a random sample of 2000 men and women constituted the real data. Based on the results of the simulation analysis: The NLM revealed 88% of DIF and 97% of DDF, on average. the Type I error rates is very close to the theoretically expected values, although it showed some inflation in unequal distribution conditions. according to the findings, the detection rate was influenced by the item parameters(difficulty and slope) and the DIF or DDF levels. Based on real data analysis, 2 items represented both DIF(Large and Medium) and DDF (Partial to Moderate) simultaneously, whereas in the NRM approach, 11 items detected as DIF/DDF; so, as expected the approaches based on “divided by distractor” strategy, fewer items were detected as DIF/DDF. The NLM while separating the DDF from the DIF test, allows for a clear evaluation of whether the distractor may be responsible for DIF. Since high-stakes tests have a special role in selection and DIF and DDF analyzes have a special place in determining the validity and measurement invariance of these exam items, it is recommended to screen the bias items, DIF/DDF comprehensive analyzes based on NLM be used.