On ignoring the heterogeneity in spatial autocorrelation: consequences and solutions

Abstract

Spatial autoregressive (SAR) models are often used to explicitly account for the spatial dependence underlying geographic phenomena. However, traditional SAR models are specified using a single SAR coefficient, assuming constant spatial dependence over space. This assumption oversimplifies the situation where the true spatial autoregressive process varies in strength; the consequences of ignoring heterogeneous autocorrelation remain to be discussed. This study proposes a heterogeneous spatial autocorrelation model by extending the spatial lag model (SLM). The new model includes change point detection for identifying patterns of spatially varying autocorrelation strengths, a SAR coefficient matrix for representing heterogeneous spatial autocorrelation, and maximum likelihood estimation for determining multiple SAR coefficients. Monte Carlo simulations demonstrate that the proposed method is effective in modeling SAR processes with heterogeneous autocorrelation patterns, while traditional SLM inflates uncertainties in the regression coefficients when a heterogeneous autocorrelation structure is not accounted for. We further applied the new method to an empirical analysis of traffic crashes in the Greater Perth Area, Australia. The heterogeneous spatial autocorrelation model reduces model RMSE by 42% (compared with traditional SLM). Results from both simulation and empirical studies indicate that spatially varying autocorrelation strengths should be considered for SAR processes and relevant applications.