Bayesian nonparametric models for spatially indexed data of mixed type

TL;DR

This paper introduces Bayesian nonparametric models for spatial data of mixed types, effectively handling confounders and residual spatial effects in environmental epidemiology through latent variables and location-specific priors.

Contribution

It proposes a novel modeling approach that jointly captures responses and confounders using Gaussian latent variables with spatially varying mixture weights, enhancing flexibility in spatial data analysis.

Findings

Model successfully captures complex spatial dependencies.

Simulation studies demonstrate improved confounder adjustment.

Application to real data shows practical effectiveness.

Abstract

We develop Bayesian nonparametric models for spatially indexed data of mixed type. Our work is motivated by challenges that occur in environmental epidemiology, where the usual presence of several confounding variables that exhibit complex interactions and high correlations makes it difficult to estimate and understand the effects of risk factors on health outcomes of interest. The modeling approach we adopt assumes that responses and confounding variables are manifestations of continuous latent variables, and uses multivariate Gaussians to jointly model these. Responses and confounding variables are not treated equally as relevant parameters of the distributions of the responses only are modeled in terms of explanatory variables or risk factors. Spatial dependence is introduced by allowing the weights of the nonparametric process priors to be location specific, obtained as probit transformations of Gaussian Markov random fields. Confounding variables and spatial configuration have a similar role in the model, in that they only influence, along with the responses, the allocation probabilities of the areas into the mixture components, thereby allowing for flexible adjustment of the effects of observed confounders, while allowing for the possibility of residual spatial structure, possibly occurring due to unmeasured or undiscovered spatially varying factors. Aspects of the model are illustrated in simulation studies and an application to a real data set.