Spatial autocorrelation is a frequent phenomenon in ecological data and can
affect estimates of model coefficients and inference from statistical models. Here,
we test the performance of three different simultaneous autoregressive (SAR) model
types (spatial error
) and common
ordinary least squares (OLS) regression when accounting for spatial autocorrelation
in species distribution data using four artificial data sets with known (but different)
spatial autocorrelation structures.
We evaluate the performance of SAR models by examining spatial
patterns in model residuals (with correlograms and residual maps), by comparing
model parameter estimates with true values, and by assessing their type I error
control with calibration curves. We calculate a total of 3240 SAR models and
illustrate how the best models [in terms of minimum residual spatial autocorrelation
(minRSA), maximum model fit (
), or Akaike information criterion (AIC)] can be
identified using model selection procedures.
Our study shows that the performance of SAR models depends on model
specification (i.e. model type, neighbourhood distance, coding styles of spatial
weights matrices) and on the kind of spatial autocorrelation present. SAR model
parameter estimates might not be more precise than those from OLS regressions in
all cases. SAR
models were the most reliable SAR models and performed well in all
cases (independent of the kind of spatial autocorrelation induced and whether models
were selected by minRSA,
or AIC), whereas OLS, SAR
weak type I error control and/or unpredictable biases in parameter estimates.
models are recommended for use when dealing with
spatially autocorrelated species distribution data. SAR
always give better estimates of model coefficients than OLS, and can thus generate bias.
Other spatial modelling techniques should be assessed comprehensively to test their
predictive performance and accuracy for biogeographical and macroecological research.|