Bayesian low-rank latent-cluster regression for mixed health outcomes
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911673939394560 |
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| author | Huang, Hsin-Hsiung Kang, Suyeon |
| author_facet | Huang, Hsin-Hsiung Kang, Suyeon |
| contents | High-dimensional health and surveillance studies often involve many collinear predictors, multiple correlated outcomes of different types, and latent heterogeneity across observational units. We propose a Bayesian latent-cluster reduced-rank regression model for multivariate mixed outcomes. The model is a finite mixture of regression surfaces: each latent cluster has a cluster-specific mean shift and a low-rank coefficient matrix, yielding simultaneous clustering, dimension reduction, and component-wise interpretability. Response coordinates may be Gaussian, Bernoulli, or negative binomial. Multiplicative gamma process shrinkage adapts the effective rank within each cluster, and a WAIC-based criterion is used to tune the number of clusters and the nominal maximal rank. We establish posterior contraction for the identifiable component-specific regression surfaces and mean shifts, up to label permutation, and derive corresponding contraction for predictor-side singular subspaces. We also analyze the default label-invariant reporting pipeline based on the posterior similarity matrix: an eigenspace embedding followed by mean shift is shown to consistently recover the latent partition under an additional strong separation margin. Simulation experiments spanning all-Gaussian, all-Bernoulli, all-negative-binomial, and mixed Gaussian--Bernoulli--negative-binomial regimes show accurate recovery of the number of clusters and competitive clustering performance against $K$-means, mclust, PCA-based clustering, and a Gaussian reduced-rank mixture benchmark. We illustrate the method in three applications that show how the model separates individual-level utilization groups and produces interpretable county- and state-level cluster maps together with response-specific posterior predictive maps. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_11935 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bayesian low-rank latent-cluster regression for mixed health outcomes Huang, Hsin-Hsiung Kang, Suyeon Methodology Computation High-dimensional health and surveillance studies often involve many collinear predictors, multiple correlated outcomes of different types, and latent heterogeneity across observational units. We propose a Bayesian latent-cluster reduced-rank regression model for multivariate mixed outcomes. The model is a finite mixture of regression surfaces: each latent cluster has a cluster-specific mean shift and a low-rank coefficient matrix, yielding simultaneous clustering, dimension reduction, and component-wise interpretability. Response coordinates may be Gaussian, Bernoulli, or negative binomial. Multiplicative gamma process shrinkage adapts the effective rank within each cluster, and a WAIC-based criterion is used to tune the number of clusters and the nominal maximal rank. We establish posterior contraction for the identifiable component-specific regression surfaces and mean shifts, up to label permutation, and derive corresponding contraction for predictor-side singular subspaces. We also analyze the default label-invariant reporting pipeline based on the posterior similarity matrix: an eigenspace embedding followed by mean shift is shown to consistently recover the latent partition under an additional strong separation margin. Simulation experiments spanning all-Gaussian, all-Bernoulli, all-negative-binomial, and mixed Gaussian--Bernoulli--negative-binomial regimes show accurate recovery of the number of clusters and competitive clustering performance against $K$-means, mclust, PCA-based clustering, and a Gaussian reduced-rank mixture benchmark. We illustrate the method in three applications that show how the model separates individual-level utilization groups and produces interpretable county- and state-level cluster maps together with response-specific posterior predictive maps. |
| title | Bayesian low-rank latent-cluster regression for mixed health outcomes |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2605.11935 |