## Dray S. (2011).
*A new perspective about Moran's coefficient: spatial
autocorrelation as a linear regression problem*.
Geographical Analysis, 43:127--141.

The computation of Moran's index of spatial
autocorrelation requires the definition of a spatial
weighting matrix. The eigendecomposition of this doubly
centered matrix (i.e., one that forces the sums of all rows
and columns to equal zero) has interesting properties that
have been exploited in various contexts: distribution
properties of the Moran coefficient (MC), spatial filtering
in linear models, generalized linear models, and
multivariate analysis. In this article, this
eigendecomposition is used to propose a new view of MC
based on its interpretation in the simple context of linear
regression. I use this interpretation to demonstrate the
different properties of MC and also the inefficiency of
this index in some situations involving simultaneous
positive and negative spatial autocorrelation. I propose
some new statistics and procedures for testing spatial
autocorrelation, and conduct a simulation study to evaluate
these new approaches.

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