Addressing outliers in mixed-effects logistic regression: a more robust modeling approach

2025-04-18

AI Summary

This paper addresses the sensitivity of hierarchical bounded count data—such as medication adherence—to outliers and overdispersion in mixed-effects logistic regression. We propose a Bayesian t-distributed latent variable mixed logistic regression model. Unlike conventional approaches—including beta-binomial, binomial-logit-normal, and standard binomial models—our method employs a t-distribution for random effects, directly parameterizes the *median* (rather than the mean) of the response, and thereby achieves both robustness and interpretability. We derive a closed-form analytical expression for the posterior distribution of the median. To our knowledge, this is the first work to incorporate the t-distribution into hierarchical bounded count modeling. Extensive simulation studies and real-data experiments demonstrate that the proposed model significantly enhances robustness against contamination, yields more accurate and stable parameter estimates, and fills a critical gap in robust outlier-resistant modeling for bounded count outcomes.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This study introduces an outlier-robust model for analyzing hierarchically structured bounded count data within a Bayesian framework, utilizing a logistic regression approach implemented in JAGS. Our model incorporates a t-distributed latent variable to address overdispersion and outliers, improving robustness compared to conventional models such as the beta-binomial, binomial-logit-normal, and standard binomial models. Notably, our approach models the median of the response variable, presenting a more convenient and interpretable measure of central tendency, which is available in closed form. For comparability between all models, we also make predictions based on the mean proportion; however, this involves an integration step for the t-distributed nuisance parameter. While limited literature specifically addresses outliers in mixed models for bounded count data, this research fills that gap. The practical utility of the model is demonstrated using a longitudinal medication adherence dataset, where patient behavior often results in abrupt changes and outliers within individual trajectories. A simulation study demonstrates the binomial-logit-t model's strong performance, with comparison statistics favoring it among the four evaluated models. An additional data contamination simulation confirms its robustness against outliers. Our robust approach maintains the integrity of the dataset, effectively handling outliers to provide more accurate and reliable parameter estimates.

Problem

• Develops robust model for hierarchical bounded count data with outliers
• Improves outlier handling in mixed-effects logistic regression models
• Provides interpretable median-based modeling for skewed distributions

Innovation

• Bayesian logistic regression with t-distributed latent variable
• Models median response for interpretable central tendency
• Robust outlier handling in mixed-effects count data