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

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, this manifests as differential item functioning (DIF), where item responses differ across groups after controlling for the latent trait. This paper develops a framework for detecting DIF in ordinal scales without requiring known group labels or anchor items. We formulate a proportional-odds latent-class item response model in which individuals are assigned probabilistically to latent classes. DIF is captured through class-specific intercept and slope shifts, allowing both uniform and non-uniform DIF. Identification is achieved through an \(\ell_1\)-penalised marginal likelihood under a sparsity assumption, with estimation implemented using a tailored EM algorithm. Because class-specific slopes leave both the location and scale of each latent class unidentified, sparsity anchors the latent metric while selecting DIF effects. Simulation studies demonstrate accurate recovery of item parameters and both types of DIF. An empirical application to a personality test reveals latent subgroups with distinct response patterns and identifies items displaying potential class-specific measurement non-invariance. The framework provides a flexible approach for assessing measurement invariance in ordinal scales when comparison groups are unobserved or poorly defined.