Robust Estimation of Item Parameters via Divergence Measures in Item Response Theory

TL;DR

This paper introduces robust estimation methods for item response theory that minimize divergence-based objective functions, improving accuracy and robustness against aberrant responses compared to traditional MMLE.

Contribution

It proposes a flexible, divergence-based estimation framework that enhances robustness in IRT, encompassing MMLE as a special case and validated through simulations.

Findings

Proposed methods outperform existing estimators in simulations with aberrant responses.

Estimators are statistically consistent and asymptotically normal.

Influence function analysis shows increased hyperparameters reduce impact of aberrant responses.

Abstract

Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study introduces robust estimation methods for item parameters in IRT. Instead of empirically minimizing Kullback--Leibler divergence as in MMLE, the proposed approach minimizes the objective functions based on robust divergences, specifically density power divergence and {\gamma}-divergence. The resulting estimators are statistically consistent and asymptotically normal under appropriate regularity conditions. Furthermore, they offer a flexible trade-off between robustness and efficiency through hyperparameter tuning, forming a generalized estimation framework encompassing MMLE as a special case. To evaluate the effectiveness of the proposed methods, we conducted simulation experiments under various conditions, including scenarios with aberrant responses. The results demonstrated that the proposed methods surpassed existing ones in performance across various conditions. Moreover, numerical analysis of influence functions verified that increasing the hyperparameters effectively suppressed the impact of responses with low occurrence probabilities, which are potentially aberrant. These findings highlight that the proposed approach offers a robust alternative to MMLE, significantly enhancing measurement accuracy in testing and survey contexts prone to aberrant responses.