A simplified spatial+ approach to mitigate spatial confounding in multivariate spatial areal models

TL;DR

This paper introduces a simplified spatial+ method for multivariate spatial areal models that effectively mitigates spatial confounding by separating covariate components, improving estimation accuracy in real and simulated data.

Contribution

It proposes a novel simplified spatial+ approach that avoids separate spatial modeling of covariates, enhancing interpretability and efficiency.

Findings

The method reliably estimates fixed effects.

It accurately captures correlations between responses.

Performance is validated through extensive simulations.

Abstract

Spatial areal models encounter the well-known and challenging problem of spatial confounding. This issue makes it arduous to distinguish between the impacts of observed covariates and spatial random effects. Despite previous research and various proposed methods to tackle this problem, finding a definitive solution remains elusive. In this paper, we propose a simplified version of the spatial+ approach that involves dividing the covariate into two components. One component captures large-scale spatial dependence, while the other accounts for short-scale dependence. This approach eliminates the need to separately fit spatial models for the covariates. We apply this method to analyse two forms of crimes against women, namely rapes and dowry deaths, in Uttar Pradesh, India, exploring their relationship with socio-demographic covariates. To evaluate the performance of the new approach, we conduct extensive simulation studies under different spatial confounding scenarios. The results demonstrate that the proposed method provides reliable estimates of fixed effects and posterior correlations between different responses.