A Simulation Study to Assess the Effect of the Number of Response Categories on the Power of Ordinal Logistic Regression for Differential Item Functioning Analysis in Rating Scales

Abstract

Objective.The present study uses simulated data to find what the optimal number of response categories is to achieve adequate power in ordinal logistic regression (OLR) model for differential item functioning (DIF) analysis in psychometric research.Methods.A hypothetical ten-item quality of life scale with three, four, and five response categories was simulated. The power and type I error rates of OLR model for detecting uniform DIF were investigated under different combinations of ability distribution (θ), sample size, sample size ratio, and the magnitude of uniform DIF across reference and focal groups.Results.Whenθwas distributed identically in the reference and focal groups, increasing the number of response categories from 3 to 5 resulted in an increase of approximately 8% in power of OLR model for detecting uniform DIF. The power of OLR was less than 0.36 when ability distribution in the reference and focal groups was highly skewed to the left and right, respectively.Conclusions.The clearest conclusion from this research is that the minimum number of response categories for DIF analysis using OLR is five. However, the impact of the number of response categories in detecting DIF was lower than might be expected.