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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2601.17612 |
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| _version_ | 1866911396877303808 |
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| 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 |