A Hybrid Latent-Class Item Response Model for Detecting Measurement Non-Invariance in Ordinal Scales

2026-01-24

AI Summary

This study addresses the challenge of detecting differential item functioning (DIF) in ordinal-scale items when known group labels or anchor items are unavailable. The authors propose a hybrid latent class item response model that employs a proportional odds framework to model ordered responses, probabilistically assigning individuals to latent classes. Within this framework, uniform and nonuniform DIF are captured through class-specific intercept and slope deviations, respectively. The method requires no prespecified grouping variables or anchor items; instead, it leverages sparsity assumptions and L1 regularization to automatically identify DIF effects. A tailored EM algorithm is developed to optimize the L1-penalized marginal likelihood. Simulation results demonstrate accurate parameter recovery and effective DIF detection, while empirical analysis of a personality inventory reveals latent subgroups with heterogeneous response patterns and potentially biased items.

Technology Category

Reasoning under Uncertainty: Relational Probabilistic ModelsSearch and Optimization: Mixed Discrete/Continuous SearchData Mining & Knowledge Management: Anomaly/Outlier Detection

Application Category

User Modeling, Personalization and Recommendation: Fairness-aware retrieval and rankingSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingEconomics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Measurement non-invariance arises when the psychometric properties of a scale differ across subgroups, undermining the validity of group comparisons. At the item level, such non-invariance manifests as differential item functioning (DIF), which occurs when the conditional distribution of an item response differs across groups after controlling for the latent trait. This paper introduces a statistical framework for detecting DIF in ordinal scales without requiring known group labels or anchor items. We propose a hybrid latent-class item response model to ordinal data using a proportional-odds formulation, assigning individuals probabilistically to latent classes. DIF is captured through class-specific shifts in item intercepts and slopes, allowing for both uniform and non-uniform DIF. The identification of DIF effects is achieved via an $L_1$-penalised marginal likelihood function under a sparsity assumption, and model estimation is implemented using a tailored EM algorithm. Simulation studies demonstrate strong recovery of item parameters and both uniform and non-uniform types of DIF. An empirical application to a personality test reveals latent subgroups with distinct response patterns and identifies items that may bias group comparisons. The proposed framework provides a flexible approach to assessing measurement invariance in ordinal scales when comparison groups are unobserved or poorly defined.

Problem

• measurement non-invariance
• differential item functioning
• ordinal scales
• latent subgroups
• group comparisons

Innovation

• latent class
• differential item functioning
• ordinal item response theory
• measurement invariance
• L1 regularization