Latent Impact and Differential Item Functioning Analysis for Asymmetric IRT Models

2026-05-07

AI Summary

This study addresses the challenge of jointly modeling latent group effects and differential item functioning (DIF) in measurement invariance assessment when group membership is unobserved and anchor items are unavailable. The authors propose a novel approach grounded in asymmetric item response theory (IRT), integrating a mixture IRT model with an ℓ₁-regularized estimator. By introducing latent classes to capture population heterogeneity and item-specific shifts to represent DIF effects, the method simultaneously identifies latent groups and DIF items without requiring known group labels or pre-specified anchor items. This work represents the first effort to achieve joint estimation of latent impact and DIF within an asymmetric IRT framework under completely unsupervised conditions, thereby overcoming limitations imposed by traditional symmetric link functions and reliance on anchor items. Simulation and empirical analyses demonstrate that the proposed method accurately recovers underlying parameter structures and successfully distinguishes between pure latent impact and pronounced DIF in educational assessments.

Abstract

Differential item functioning (DIF) arises alongside latent population heterogeneity in many applications, and both must be accounted for when assessing measurement invariance. In many practical settings, however, the comparison groups are unobserved and anchor items are unknown. A further challenge is that item response theory models traditionally assume symmetric link functions, yet empirical response processes may exhibit substantial asymmetry. This paper proposes a general framework for jointly analysing impact and DIF under asymmetric item response models. Unobserved group differences are represented by latent classes within a mixture item response model, while item-specific shifts capture DIF effects. Assuming the number of DIF items is relatively small, an $\ell_1$-regularised estimator is used to simultaneously identify the latent classes and select DIF items without requiring observed group labels or pre-specified anchor items. A simulation study evaluates recovery of impact, item parameters, and DIF effects across a range of configurations. The method is illustrated using two empirical applications from educational testing. In one dataset, the selected model reveals both impact and item-level DIF, whereas in the other, the results indicate substantial impact but little evidence of item-level DIF.

Problem

• differential item functioning
• latent impact
• asymmetric IRT models
• measurement invariance
• unobserved groups

Innovation

• asymmetric IRT
• differential item functioning
• latent impact
• mixture IRT model
• L1 regularization