Marginally interpretable spatial logistic regression with bridge processes

2024-12-06

AI Summary

In spatial logistic regression, incorporating random effects to account for spatial dependence shifts coefficient interpretation from population-averaged to subject-specific, thereby forfeiting marginal interpretability. To address this, we propose a bridge-process-based spatial logistic regression model that embeds spatially structured random effects without compromising marginal interpretability. This bridge process is the first spatial random-effects formulation that simultaneously preserves both marginal and conditional interpretations, and admits a scale-mixture-of-normals representation with favorable theoretical properties. Using Bayesian inference and an efficient MCMC algorithm, our model achieves superior predictive accuracy, computational efficiency, and interpretability in simulation studies and analysis of Gambian childhood malaria data. The framework establishes a new paradigm for modeling spatial binary data—rigorous from a statistical standpoint while retaining practical, policy-relevant interpretability.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Statistical Relational/Logic Learning
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

In including random effects to account for dependent observations, the odds ratio interpretation of logistic regression coefficients is changed from population-averaged to subject-specific. This is unappealing in many applications, motivating a rich literature on methods that maintain the marginal logistic regression structure without random effects, such as generalized estimating equations. However, for spatial data, random effect approaches are appealing in providing a full probabilistic characterization of the data that can be used for prediction. We propose a new class of spatial logistic regression models that maintain both population-averaged and subject-specific interpretations through a novel class of bridge processes for spatial random effects. These processes are shown to have appealing computational and theoretical properties, including a scale mixture of normal representation. The new methodology is illustrated with simulations and an analysis of childhood malaria prevalence data in the Gambia.

Problem

• Maintains both population-averaged and subject-specific interpretations in spatial logistic regression
• Introduces bridge processes for spatial random effects to preserve interpretability
• Provides a full probabilistic model for spatial data with computational advantages

Innovation

• Bridge processes for spatial random effects
• Maintains both population-averaged and subject-specific interpretations
• Scale mixture of normal representation for computational efficiency