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This package provides a number of useful functions that facilitate
the analysis of spatially autocorrelated data based on the eigenfunction
decomposition of an exogenously given connectivity matrix
W. The main function getEVs()
specifies a projection matrix M and
symmetrizes the connectivity matrix by
V=1/2*(W+W’)
before decomposing the transformed matrix MVM.
If covariates are supplied, this function constructs the projection
matrix by:
M=I-X(X’X)-1
X’. Eigenvectors obtained from this
specification are not only mutually uncorrelated but also orthogonal to
the covariates in X. In contrast, if no
covariates are supplied, the projection matrix simplifies to
M=
I-11’/n,
where 1 is a vector of ones and n is
the number of units. Besides the eigenvectors and eigenvalues,
getEVs() also provides the Moran coefficient associated
with each eigenvector.
Subsequently, these eigenvectors can be used to perform
semiparametric spatial filtering in a regression framework. The
functions lmFilter() and glmFilter() in this
package implement unsupervised eigenvector selection based on a stepwise
regression procedure and different objective functions, including i) the
maximization of model fit, ii) minimization of residual autocorrelation,
iii) the statistical significance of residual autocorrelation, and iv)
the statistical significance of candidate eigenvectors. If other
selection criteria are required or a model needs to be fitted that is
currently not supported by these two functions, supervised eigenvector
selection can be performed as well using the basic stats::lm()
and stats::glm()
commands in conjunction with the output generated by
getEVs(). This option provides additional flexibility.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.