A comparison of simultaneous autoregressive and generalized least squares models for dealing with spatial autocorrelation

In their recent paper, Kissling & Carl (2008) recommended the spatial error simultaneous autoregressive model (SAR(err)) over ordinary least squares (OLS) for modelling species distribution. We compared these models with the generalized least squares model (GLS) and a variant of SAR (SAR(vario)). GLS and SAR(vario) are superior to standard implementations of SAR because the spatial covariance structure is described by a semivariogram model. We used the complete datasets employed by Kissling & Carl (2008), with strong spatial autocorrelation, and two datasets in which the spatial structure was degraded by sample reduction and grid coarsening. GLS performed consistently better than OLS, SAR(err) and SAR(vario) in all datasets, especially in terms of goodness of fit. SAR(vario) was marginally better than SAR(err) in the degraded datasets. GLS was more reliable than SAR-based models, so its use is recommended when dealing with spatially autocorrelated data.