Model-Agnostic Influential Outlier Detection for Mixed Effects and Multi-Level Models
Abstract
Influential Outlier Detection is developed for mixed-effects models on clustered data. The Influential Outlier Metric is defined as a combination of SHapley Additive exPlanantion (SHAP) values and model residuals, both of which undergo a change of measure transformation. Building on previous work showcasing the suitability of using Normalizing flows to map arbitrary distributions to a flexible base distribution for statistical inference, the Normalizing Flows are constructed to allows contextual information and also provide a goodness of fit diagnostic for model evaluation. The use of SHAP values in the construction moves away from model specific tools and instead provides point-wise model agnostic influential outlier. The advantages and limitations of this approach are examined in several models including the linear model, the random forest, and gradient-boosted trees.
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BibTeX
@misc{jones2026modelagnostic,
title = {{Model-Agnostic Influential Outlier Detection for Mixed Effects and Multi-Level Models}},
author = {Colin C Jones and David A Campbell and Yan Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01720},
eprint = {2610.01720},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01720},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Model-Agnostic Influential Outlier Detection for Mixed Effects and Multi-Level Models
AU - Colin C Jones
AU - David A Campbell
AU - Yan Liu
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01720
UR - https://arxiv.org/abs/2610.01720
AB - Influential Outlier Detection is developed for mixed-effects models on clustered data. The Influential Outlier Metric is defined as a combination of SHapley Additive exPlanantion (SHAP) values and model residuals, both of which undergo a change of measure transformation. Building on previous work showcasing the suitability of using Normalizing flows to map arbitrary distributions to a flexible base distribution for statistical inference, the Normalizing Flows are constructed to allows contextual information and also provide a goodness of fit diagnostic for model evaluation. The use of SHAP values in the construction moves away from model specific tools and instead provides point-wise model agnostic influential outlier. The advantages and limitations of this approach are examined in several models including the linear model, the random forest, and gradient-boosted trees.
ER -