Abstract
In this simulation study, regressions specified with autocorrelation effects are compared against those with relationship heterogeneity effects, and in doing so, provides guidance on their use. Regressions investigated are: (1) multiple linear regression, (2) a simultaneous autoregressive error model, and (3) geographically weighted regression. The first is nonspatial and acts as a control, the second accounts for stationary spatial autocorrelation via the error term, while the third captures spatial heterogeneity through the modeling of nonstationary relationships between the response and predictor variables. The geostatistical‐based simulation experiment generates data and coefficients with known multivariate spatial properties, all within an area‐unit spatial setting. Spatial autocorrelation and spatial heterogeneity effects are varied and accounted for. On fitting the regressions, that each have different assumptions and objectives, to very different geographical processes, valuable insights to their likely performance are uncovered. Results objectively confirm an inherent interrelationship between autocorrelation and heterogeneity, that results in an identification problem when choosing one regression over another. Given this, recommendations on the use and implementation of these spatial regressions are suggested, where knowledge of the properties of real study data and the analytical questions being posed are paramount.
Highlights
As outlined in Anselin (1988), and reviewed in Goodchild (2004); Anselin (2010), two core effects need to be considered when fitting a regression to spatial data, one of spatial autocorrelation (e.g., Cressie 1993; LeSage and Pace 2009) and one of spatial heterogeneity with respect to data relationships (e.g., Fotheringham, Brunsdon, and Charlton 2002; LeSage and Pace 2009)
Given the specified characteristics are reasonable, results objectively confirm a strong interrelationship between autocorrelation and relationship heterogeneity
multiple linear regression (MLR) fit to a nonstationary coefficient process will tend to produce autocorrelated residuals, ensuring a simultaneous autoregressive error model (SAR) fit to be a reasonable, but incorrect model choice
Summary
Rothamsted Research, SSGS, North Wyke, Okehampton EX20 2SB, United Kingdom of Great Britain and Northern Ireland. In this simulation study, regressions specified with autocorrelation effects are compared against those with relationship heterogeneity effects, and in doing so, provides guidance on their use. Regressions investigated are: (1) multiple linear regression, (2) a simultaneous autoregressive error model, and (3) geographically weighted regression. The first is nonspatial and acts as a control, the second accounts for stationary spatial autocorrelation via the error term, while the third captures spatial heterogeneity through the modeling of nonstationary relationships between the response and predictor variables. The geostatistical-based simulation experiment generates data and coefficients with known multivariate spatial properties, all within an area-unit spatial setting. Recommendations on the use and implementation of these spatial regressions are suggested, where knowledge of the properties of real study data and the analytical questions being posed are paramount
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