R/getEVs.R
getEVs.RdExtract eigenvectors and corresponding eigenvalues from the matrix MWM, where M denotes a symmetric and idempotent projection matrix and W is the spatial connectivity matrix. This function also reports the Moran coefficient associated with each of the eigenvectors.
getEVs(W, covars = NULL)spatial connectivity matrix
vector/ matrix of regressors included in the construction of the projection matrix M - see Details
A list containing the following objects:
vectorsmatrix of all eigenvectors
valuesvector of the corresponding eigenvalues
moranvector of the Moran coefficients associated with the eigenvectors
The eigenfunctions obtained by getEVs
can be used to perform supervised eigenvector selection and to
manually create a spatial filter. To this end, a candidate set
may be determined by 1) the sign of the spatial autocorrelation
in model residuals and 2) the strength of spatial association
found in each eigenvector as indicated by moran.
Prior to the spectral decomposition, getEVs symmetrizes the
spatial connectivity matrix by: 1/2 * (W + W').
If covars are supplied, the function uses the covariates to construct
projection matrix: M = I - X (X'
X)^-1X'. Using this matrix results in a set of
eigenvectors that are uncorrelated to each other as well as to the
covariates. If covars = NULL, only the intercept term is used
to construct M. See e.g., Griffith and Tiefelsdorf (2007)
for more details on the appropriate choice of M.
Tiefelsdorf, Michael and Daniel A. Griffith (2007): Semiparametric filtering of spatial autocorrelation: the eigenvector approach. Environment and Planning A: Economy and Space, 39 (5): pp. 1193 - 1221.
data(fakedata)
E <- getEVs(W = W, covars = NULL)