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.