Optimizing the choice of a spatial weighting matrix in eigenvector-based methods.

Eigenvector-mapping methods such as Moran's eigenvector maps (MEM) are derived from a spatial weighting matrix (SWM) that describes the relations among a set of sampled sites. The specification of the SWM is a crucial step, but the SWM is generally chosen arbitrarily, regardless of the sampling design characteristics. Here, we compare the statistical performances of different types of SWMs (distance-based or graph-based) in contrasted realistic simulation scenarios. Then, we present an optimization method and evaluate its performances compared to the arbitrary choice of the most-widely used distance-based SWM. Results showed that the distance-based SWMs generally had lower power and accuracy than other specifications, and strongly underestimated spatial signals. The optimization method, using a correction procedure for multiple tests, had a correct type I error rate, and had higher power and accuracy than an arbitrary choice of the SWM. Nevertheless, the power decreased when too many SWMs were compared, resulting in a trade-off between the gain of accuracy and the loss of power. We advocate that future studies should optimize the choice of the SWM using a small set of appropriate candidates. R functions to implement the optimization are available in the adespatial package and are detailed in a tutorial.