Predicting the magnitude of residual spatial autocorrelation in geographical ecology

Abstract

The level of spatial autocorrelation (SAC) present in model residuals can have a detrimental influence on statistical inferences in geographical ecology. There has been significant progress in understanding the nature and causes of residual SAC and developing new methods to reduce the SAC. However, ecologists have not yet found a suitable answer as to when the level of residual autocorrelation is likely to magnify and whether its shift through spatial regression (i.e. the difference in the residual SAC produced by non‐spatial and spatial approaches) can be predicted using a set of readily available variables. In this paper, I reanalyzed the outcomes reported by Bini et al. (2009), who originally compared the differences in the standardized regression coefficients resulting from non‐spatial ordinary least squares and various spatially explicit methods. Although these researchers were unable to identify reliable predictors of the coefficient shifts, in the present study, I observed that the level of residual autocorrelation significantly and linearly increased with an increase in the magnitude of the SAC inherently possessed by, especially, response and explanatory variables. Moreover, the amount of shift in the residual SAC varied as a linear function of the response and explanatory variables. These findings imply that, in general, specific conditions exist under which there is an increase in the magnitude of the residual SAC, that such a shift can be predicted by the nature and structure of the data sets involved, and that, after all, the residual SAC varies systematically regardless of the selection of the data type, statistical method and spatial scale. I suggest that the level of the SAC present in the input variables can directly indicate how much improvement (i.e. reduction in the residual SAC) a non‐spatial model will experience when a proper spatial approach is employed.