Linear regression in ecological studies involving space: methodology and an application example in public health

Many health-related phenomena can be better understood when the geographic region in which they occur is taken into account. One of the most important aspects to consider in spatial study designs is the presence of autocorrelation in observations measured across space. If this spatial dependence is not properly modeled, the resulting statistics may be biased, compromising the validity of conclusions regarding the presence or absence of associations. Methodologies developed based on the linear regression model allow this dependence to be adequately accommodated, producing precise, robust, and unbiased estimates. With the aim of highlighting the applicability of spatial models and pointing out the necessary precautions in data analysis, this article describes, step by step, one of the most commonly used methodologies for spatial data analysis, as well as the measures to be taken to avoid modeling errors and distortion of results. The linear regression model is presented, along with procedures to evaluate model fit, the most commonly used measure to detect spatial dependence, and two autoregressive models frequently applied to model this dependence (SAR and SEM). An application example is provided using the GeoDa and R software.