Tractable Bayes of Skew-Elliptical Link Models for Correlated Binary Data

TL;DR

This paper introduces a Bayesian multivariate skew-elliptical link model for correlated binary data, offering a flexible alternative to the probit model, with closed-form posteriors and demonstrated application to COVID-19 data.

Contribution

It proposes a new skew-elliptical link model with closed-form Bayesian posteriors, extending the multivariate probit model to better handle imbalanced binary data.

Findings

Skew-elliptical model fits COVID-19 data better than probit.

Spatial dependence is significant in modeling COVID-19 spikes.

The model captures asymmetry in binary response data.

Abstract

Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior. The new methodology is illustrated by application to COVID-19 pandemic data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides better fit to our highly imbalanced dataset.