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

TL;DR

This paper presents a new statistical framework using a hybrid latent-class item response model to detect measurement non-invariance and differential item functioning in ordinal scales without predefined group labels, enhancing validity of group comparisons.

Contribution

It introduces a novel hybrid latent-class IRT model with an $L_1$-penalised likelihood for detecting DIF without known groups or anchor items, applicable to ordinal data.

Findings

Simulation studies show accurate recovery of item parameters and DIF types.

Application to personality data reveals latent subgroups and biased items.

Framework effectively assesses measurement invariance in unobserved groups.

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.