Tractable Bayes of skew-elliptical link models for correlated binary data

Area of Science:

• Statistics
• Biostatistics
• Epidemiology

Background:

• Correlated binary response data are common in longitudinal and spatial studies.
• The multivariate probit model is a standard but may be limited with imbalanced data.
• A symmetric link function may not capture complex dependencies in skewed data.

Purpose of the Study:

• To propose a novel multivariate skew-elliptical link model for correlated binary responses.
• To extend existing models for improved flexibility with imbalanced datasets.
• To provide a robust statistical framework for analyzing complex health data.

Main Methods:

• Development of a multivariate skew-elliptical link model.
• Bayesian inference for parameter estimation.
• Application to COVID-19 weekly new case data from California counties.

Main Results:

• The proposed model includes the multivariate probit model as a special case.
• Regression coefficients exhibit a closed-form unified skew-elliptical posterior.
• Analysis of COVID-19 data highlights the importance of spatial dependence and model flexibility for imbalanced data.

Conclusions:

• The multivariate skew-elliptical model offers enhanced flexibility over the standard multivariate probit model.
• The model provides a better fit for highly imbalanced datasets.
• Spatial dependence is crucial when modeling extreme spikes in infectious disease data.