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

Gabriel Wallin, Qi Huang|arXiv (Cornell University)|Jan 24, 2026

Psychometric Methodologies and Testing0 citations

TL;DR

The paper develops a regularised proportional-odds latent-class IRT model to detect differential item functioning in ordinal scales without known group labels, using an ℓ1-penalised marginal likelihood and an EM algorithm.

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.

Motivation & Objective

• Motivate the need to detect measurement non-invariance across subgroups in ordinal scales.
• Develop a framework that does not require known group labels or anchor items.
• Propose a proportional-odds latent-class item response model with probabilistic class assignment.
• Incorporate ℓ1-penalised marginal likelihood to identify DIF under sparsity assumptions.
• Provide an estimation algorithm tailored for this model and demonstrate its effectiveness.

Proposed method

• Formulate a proportional-odds latent-class IRT model where individuals are probabilistically assigned to latent classes.
• Model DIF via class-specific intercept and slope shifts to capture uniform and non-uniform DIF.
• Identify parameters using an ℓ1-penalised marginal likelihood under a sparsity assumption.
• Estimate parameters with a tailored expectation-maximization (EM) algorithm.
• Anchor latent metric via sparsity to address identification issues arising from class-specific slopes.
• Evaluate performance through simulation studies and an empirical application.

Experimental results

Research questions

• RQ1 Can DIF be detected in ordinal scales without known group labels or anchor items?
• RQ2 Do class-specific intercepts and slopes adequately capture uniform and non-uniform DIF?
• RQ3 Does an ℓ1-penalised marginal likelihood effectively recover item parameters and DIF structure?
• RQ4 Is the proposed EM algorithm capable of estimating the regularised latent-class IRT model accurately?

Key findings

• Simulation studies show accurate recovery of item parameters and both types of DIF.
• Latent subgroups with distinct response patterns can be identified in empirical data.
• Items displaying potential class-specific measurement non-invariance are detected in the empirical application.