Advancing Polytomous DIF Detection with the Residual DIF Framework

초록

Lim et al. (2022) introduced the residual-based differential item functioning (RDIF) detection framework, comprising RDIFR, RDIFS, and RDIFRRS statistics, each specifically designed to test uniform, nonuniform, and mixed DIF, respectively. The RDIF framework offers a multitude of advantages, including minimal computational demand, satisfactory power, well-controlled Type I error rates, and the elimination of the need for group-specific item calibrations, IRT equating, or sequential model fitting. Building on this, Lim et al. (2023a) demonstrated the adaptability of the RDIF framework for DIF screening in computerized adaptive tests, while Lim et al. (2023b) further broadened its scope, showing its applicability in detecting DIF across multiple groups. This study contributes to the RDIF literature by introducing two additional unique approaches suitable for polytomous DIF detection. Computational summaries for the two approaches, for an item with five score categories, is given below: (1) Using aggregated item score data, compute residuals between observed item scores (e.g., 2) and model-predicted scores (e.g., 2.5). (2) Using individual score category data, calculate residuals between one-hot encoding vectors (e.g., [0, 0, 1, 0, 0] for an observed score of 2) and the corresponding probability vectors (e.g., [.1, .2, .4, .25, .05]), representing the probability of endorsing each score category. Preliminary simulation results suggest that both extended versions of the RDIF framework effectively maintain well-controlled Type I error rates and have sufficient power. Additionally, their notably swifter implementation compared to other IRT-based methods positions them as practical and efficient tools for evaluating DIF in polytomous items.