spdep (version 0.2-3)

eigenw: Spatial weights matrix eigenvalues

Description

The function returns a numeric vector of eigenvalues of the weights matrix generated from the spatial weights object listw. The eigenvalues are used to speed the computation of the Jacobian in spatial SAR model estimation:

$$\log(\det[I - \rho W]) = \log\prod_{i=1}^{n}(1 - \rho \lambda_i)$$

where $W$ is the n by n spatial weights matrix, and $\lambda_i$ are the eigenvalues of $W$.

Usage

eigenw(listw, quiet=TRUE)

Arguments

listw

a listw object created for example by nb2listw

quiet

set to FALSE for short summary

Value

• a numeric vector of eigenvalues of the weights matrix generated from the spatial weights object listw.

References

Cliff, A. D., Ord, J. K. 1981 Spatial processes, Pion, p. 155; Ord, J. K. 1975 Estimation methods for models of spatial interaction, Journal of the American Statistical Association, 70, 120-126.

See Also

eigen,

Examples

data(oldcol)
W.eig <- eigenw(nb2listw(COL.nb, style="W"))
1/range(W.eig)
S.eig <- eigenw(nb2listw(COL.nb, style="S"))
1/range(S.eig)
B.eig <- eigenw(nb2listw(COL.nb, style="B"))
1/range(B.eig)