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[2602.21572] Goodness-of-Fit Tests for Latent Class Models with Ordinal Categorical Data
Summary
This article presents a new goodness-of-fit test for latent class models applied to ordinal categorical data, addressing the challenge of estimating the correct number of latent classes from data.
Why It Matters
Understanding the number of latent classes in statistical models is crucial for accurate data interpretation in fields like psychology and education. This research provides a robust statistical method that enhances model reliability and aids researchers in drawing valid conclusions from their data.
Key Takeaways
- Introduces a novel test statistic for latent class models.
- Addresses the challenge of determining the number of latent classes.
- Demonstrates the effectiveness of the proposed method through extensive experiments.
- Provides sequential testing algorithms for consistent estimation.
- Highlights the application of the model in social sciences.
Statistics > Machine Learning arXiv:2602.21572 (stat) [Submitted on 25 Feb 2026] Title:Goodness-of-Fit Tests for Latent Class Models with Ordinal Categorical Data Authors:Huan Qing View a PDF of the paper titled Goodness-of-Fit Tests for Latent Class Models with Ordinal Categorical Data, by Huan Qing View PDF HTML (experimental) Abstract:Ordinal categorical data are widely collected in psychology, education, and other social sciences, appearing commonly in questionnaires, assessments, and surveys. Latent class models provide a flexible framework for uncovering unobserved heterogeneity by grouping individuals into homogeneous classes based on their response patterns. A fundamental challenge in applying these models is determining the number of latent classes, which is unknown and must be inferred from data. In this paper, we propose one test statistic for this problem. The test statistic centers the largest singular value of a normalized residual matrix by a simple sample-size adjustment. Under the null hypothesis that the candidate number of latent classes is correct, its upper bound converges to zero in probability. Under an under-fitted alternative, the statistic itself exceeds a fixed positive constant with probability approaching one. This sharp dichotomous behavior of the test statistic yields two sequential testing algorithms that consistently estimate the true number of latent classes. Extensive experimental studies confirm the theoretical findings and demonstrate t...
