Saved in:
Bibliographic Details
Main Authors: Wallin, Gabriel, Huang, Qi
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2601.17612
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866911396877303808
author Wallin, Gabriel
Huang, Qi
author_facet Wallin, Gabriel
Huang, Qi
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2601_17612
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A Hybrid Latent-Class Item Response Model for Detecting Measurement Non-Invariance in Ordinal Scales
Wallin, Gabriel
Huang, Qi
Methodology
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.
title A Hybrid Latent-Class Item Response Model for Detecting Measurement Non-Invariance in Ordinal Scales
topic Methodology
url https://arxiv.org/abs/2601.17612