Bridging conditional and marginal inference for spatially referenced binary data.

Area of Science:

• Epidemiology
• Biostatistics
• Spatial Statistics

Background:

• Spatially referenced binary data are prevalent in public health.
• Logistic regression is a natural model for binary data due to its log-odds interpretation.
• Standard Gaussian spatial random effects in logistic regression can obscure the interpretation of coefficients when marginalizing over random effects.

Purpose of the Study:

• To propose a new spatial random effect distribution using a copula framework.
• To ensure regression coefficients maintain their log-odds interpretation both conditionally and marginally.
• To provide a more interpretable and generalizable model for spatial epidemiological data.

Main Methods:

• Developed a novel spatial random effect distribution within a copula framework.
• Applied the proposed methodology to logistic regression models for spatial binary data.
• Conducted simulations to evaluate the robustness of the approach.

Main Results:

• The proposed copula-based approach ensures that regression coefficients retain their log-odds interpretation.
• The methodology demonstrated robustness across various random effect scenarios in simulations.
• The approach was successfully applied to a real-world dataset on periodontal health.

Conclusions:

• The copula framework offers a flexible solution for spatial logistic regression, preserving coefficient interpretability.
• This method enhances the generalization of findings across different spatial regions.
• The approach is suitable for diverse spatial datasets, including areal and geostatistical data, and hierarchical models.