A Proposal for Homoskedastic Modeling With Conditional Auto-Regressive Distributions

Conditional auto-regressive (CAR) distributions are widely used to deal with spatial dependence in the geographic analysis of areal data. These distributions establish multivariate dependence networks by defining conditional relationships between neighboring units, resulting in positive dependence among nearby observations. Despite their practical convenience and well-founded principles, the conditional nature of CAR distributions can lead to undesirable marginal properties, such as inherent heteroskedasticity assumptions that may significantly impact the posterior distributions. In this paper, we highlight the variance issues associated with CAR distributions, particularly focusing on edge effects and issues related to the region's geometry. We show that edge effects may be more pronounced and widespread in disease mapping studies than previously anticipated. To address these heteroskedasticity concerns, we introduce a new conditional autoregressive distribution designed to mitigate these problems. We demonstrate how this distribution effectively diminishes the practical issues identified in earlier models.