Function to compute extreme values of Moran's I

This function computes the upper and lower bounds of Moran's I for a given spatial weighting matrix (stored in a listw object). These values are obtained by the eigendecomposition of the spatial weighting matrix.

moran.bounds(listw)

Arguments

listw

an object of class listw

Value

A vector containing the maximum and minimum of Moran's I for a given spatial weighting matrix value returned

References

de Jong, P., Sprenger, C., & van Veen, F. (1984). On extreme values of Moran's I and Geary's C. Geographical Analysis, 16(1), 17-24.

See also

mem nb2listw

Author

Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

if(require("ade4", quietly = TRUE)){
 if(require("spdep", quietly = TRUE)){
     data(oribatid)
     nbtri <- tri2nb(as.matrix(oribatid$xy))
     lwB <- nb2listw(nbtri, style = "B")
     lwW <- nb2listw(nbtri, style = "W")
     scB <- mem(lwB)
     scW <- mem(lwW)
     moran.bounds(lwB)
     moran.mc(scB[,1], lwB, 9)
     moran.mc(scB[,69], lwB, 9)
     moran.bounds(lwW)
     moran.mc(scW[,1], lwW, 9)
     moran.mc(scW[,69], lwW, 9)
 }
}
#> 
#> 	Monte-Carlo simulation of Moran I
#> 
#> data:  scW[, 69] 
#> weights: lwW  
#> number of simulations + 1: 10 
#> 
#> statistic = -0.5473, observed rank = 1, p-value = 0.9
#> alternative hypothesis: greater
#>