From Ord's 1975 paper, it is known that the Jacobian for SAR models may be found by "symmetrizing" by similarity (the eigenvalues of similar matrices are identical, so the Jacobian is too). This applies only to styles "W" and "S" with underlying symmetric binary neighbour relations or symmetric general neighbour relations (so no k-nearest neighbour relations). The function is invoked automatically within the SAR fitting functions, to call eigen on a symmetric matrix for the default eigen method, or to make it possible to use the Matrix method on weights that can be "symmetrized" in this way.

similar.listw(listw)

## Arguments

listw a listw object created for example by nb2listw

## Value

a listw object

## References

Ord, J. K. 1975 Estimation methods for models of spatial interaction, Journal of the American Statistical Association, 70, 120-126

## Author

Roger Bivand Roger.Bivand@nhh.no

lagsarlm, errorsarlm

## Examples

#require("spdep", quietly=TRUE)
data(oldcol, package="spdep")
COL.W <- spdep::nb2listw(COL.nb, style="W")
COL.S <- spdep::nb2listw(COL.nb, style="S")
sum(log(1 - 0.5 * eigenw(COL.W)))
#> [1] -1.62766
sum(log(1 - 0.5 * eigenw(similar.listw(COL.W))))
#> [1] -1.62766
W_J <- as(as_dsTMatrix_listw(similar.listw(COL.W)), "CsparseMatrix")
I <- as_dsCMatrix_I(dim(W_J)[1])
c(determinant(I - 0.5 * W_J, logarithm=TRUE)$modulus) #> [1] -1.62766 sum(log(1 - 0.5 * eigenw(COL.S))) #> [1] -1.602757 sum(log(1 - 0.5 * eigenw(similar.listw(COL.S)))) #> [1] -1.602757 W_J <- as(as_dsTMatrix_listw(similar.listw(COL.S)), "CsparseMatrix") c(determinant(I - 0.5 * W_J, logarithm=TRUE)$modulus)
#> [1] -1.602757