Graph-theoretic Inference for Random Effects in High-dimensional Studies
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915333893259264 |
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| author | Chu, Lynna Bai, Yichuan |
| author_facet | Chu, Lynna Bai, Yichuan |
| contents | We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero. Our approach is non-parametric and model-free in the sense that we not require correct specification of the mixed model nor estimation of unknown parameters. Instead, the test statistic evaluates whether incorporating group-level correlation meaningfully improves the ability of a potentially high-dimensional covariate vector $X$ to predict a response variable $Y$. We establish the consistency of the proposed test and derive its asymptotic null distribution. Through simulation studies and a real data application, we demonstrate the practical effectiveness of the proposed test. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_07946 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Graph-theoretic Inference for Random Effects in High-dimensional Studies Chu, Lynna Bai, Yichuan Methodology We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero. Our approach is non-parametric and model-free in the sense that we not require correct specification of the mixed model nor estimation of unknown parameters. Instead, the test statistic evaluates whether incorporating group-level correlation meaningfully improves the ability of a potentially high-dimensional covariate vector $X$ to predict a response variable $Y$. We establish the consistency of the proposed test and derive its asymptotic null distribution. Through simulation studies and a real data application, we demonstrate the practical effectiveness of the proposed test. |
| title | Graph-theoretic Inference for Random Effects in High-dimensional Studies |
| topic | Methodology |
| url | https://arxiv.org/abs/2506.07946 |