A Bayesian shared-effects modeling framework to quantify the modifiable areal unit problem

Abstract

The modifiable areal unit problem (MAUP) refers to the effects caused by modifying the units of analysis in the context of spatial statistical analyses on areal data. The problem was formulated decades ago, but it is still of interest due to its complexity. Usually, studies on the MAUP are experimental, focusing mainly on analyzing the variation of model estimates or statistical properties as a consequence of varying the units of analysis. Indeed, the theoretical advances in this research line are scarce, leaving the MAUP as an issue to be considered in practice if spatial analyses are carried out at different scales or with multiple zonations of the study area. In this paper, a Bayesian shared-effects modeling framework is proposed for quantifying the MAUP, both globally and locally. In a global sense, the model described allows measuring the discrepancy in a covariate effect between two different spatial scales. If a global MAUP effect is identified, posterior predictive checks can be computed to detect those spatial units that contribute the most to such discrepancies. The methodology proposed is applied first to a traffic accident dataset recorded in Valencia, Spain, including multiple environmental and sociodemographic covariates. Five different partitions of the city based on the structure of census tracts are considered to analyze MAUP effects. A second application is also shown, considering a dataset about COVID-19 death counts in the Greater London area at two different aggregation levels. This second dataset includes multiple socioeconomic and health indicators as well.