With \(S_r(W) = (I - \rho W)^{-1}(\beta_r I + \theta_r W)\), average
direct \(tr(S_r)/n\), total \(1'S_r 1/n\), indirect their difference
(LeSage and Pace 2009), as spatialreg::impacts with the exact
inverse. beta and theta exclude the intercept.
Usage
SpatialImpacts(rho, beta, W, theta = NULL)
Arguments
- rho
Spatial autoregressive parameter.
- beta
Coefficients of the covariates.
- W
Spatial weights matrix.
- theta
Coefficients of the lagged covariates (Durbin), or NULL.
Value
List with direct, indirect, total.
References
LeSage, J. and Pace, R. K. (2009). Introduction to Spatial
Econometrics. CRC Press, Boca Raton.
Examples
W <- matrix(c(0, .5, 0, 1, 0, 1, 0, .5, 0), 3)
SpatialImpacts(0.4, 2, W)
#> $direct
#> [1] 2.253968
#>
#> $indirect
#> [1] 1.079365
#>
#> $total
#> [1] 3.333333
#>
