A robust mixed-effects quantile regression model using generalized Laplace mixtures to handle outliers and skewness

2025-04-20

AI Summary

Traditional mixed-effects quantile regression models (e.g., AL, GAL) for hierarchical longitudinal data suffer from sensitivity to outliers and limited flexibility in modeling skewness. To address this, we propose a contaminated generalized asymmetric Laplace (cGAL) mixed model, the first to embed a contamination mechanism within the GAL distribution. By introducing a scale-inflation component, the model automatically detects and down-weights extreme outliers without requiring pre-screening, thereby simultaneously accommodating skewness, heavy tails, and robustness. Within a Bayesian framework, inference is conducted via MCMC. In analyzing HIV viral load decay, the cGAL model substantially improves parameter estimation accuracy. Simulation studies and empirical analysis demonstrate its superior robustness over AL and GAL models, along with favorable frequentist properties—including consistency, asymptotic normality—and coherent model diagnostics.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Mixed-effects quantile regression models are widely used to capture heterogeneous responses in hierarchically structured data. The asymmetric Laplace (AL) distribution has traditionally served as the basis for quantile regression; however, its fixed skewness limits flexibility and renders it sensitive to outliers. In contrast, the generalized asymmetric Laplace (GAL) distribution enables more flexible modeling of skewness and heavy-tailed behavior, yet it remains vulnerable to extreme observations. In this paper, we extend the GAL distribution by introducing a contaminated GAL (cGAL) mixture model that incorporates a scale-inflated component to mitigate the impact of outliers without requiring explicit outlier identification or deletion. We apply this model within a Bayesian mixed-effects quantile regression framework to model HIV viral load decay over time. Our results demonstrate that the cGAL-based model more reliably captures the dynamics of HIV viral load decay, yielding more accurate parameter estimates compared to both AL and GAL approaches. Model diagnostics and comparison statistics confirm the cGAL model as the preferred choice. A simulation study further shows that the cGAL model is more robust to outliers than the GAL and exhibits favorable frequentist properties.

Problem

• Handles outliers and skewness in mixed-effects quantile regression
• Improves HIV viral load decay modeling accuracy
• Enhances robustness against extreme observations without outlier removal

Innovation

• Generalized Laplace mixtures for robust modeling
• Contaminated GAL mixture mitigates outlier impact
• Bayesian framework enhances quantile regression accuracy