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Optimizing the choice of a spatial weighting matrix in eigenvector‐based methods
Author(s) -
Bauman David,
Drouet Thomas,
Fortin MarieJosée,
Dray Stéphane
Publication year - 2018
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1002/ecy.2469
Subject(s) - weighting , set (abstract data type) , computer science , eigenvalues and eigenvectors , a weighting , mathematical optimization , algorithm , matrix (chemical analysis) , mathematics , programming language , medicine , physics , materials science , quantum mechanics , composite material , radiology
Abstract 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 SWM s (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 SWM s 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 SWM s 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.