Local G and G* of Getis and Ord

The local statistics of Getis and Ord (1992) as z values (Ord and Getis 1995): G_i compares the weighted sum of the neighbours' values with its expectation from the other n - 1 values; G*_i (star = TRUE) includes the unit itself with weight 1 and uses all n. Large positive values mark concentrations of high values, large negative ones of low values. With star = TRUE the weights are best binary (style = "raw").

Usage

locgi(x, w, star = TRUE)

Arguments

x

The values: finite numbers, one per unit.

w

The weights: spwt()'s list, or an spdep listw object, for as many units as x.

star

TRUE for G*, FALSE for G.

Value

A numeric vector of z values, one per unit; NaN for a unit without neighbours.

References

Ord, J. K. and Getis, A. (1995). Local spatial autocorrelation statistics: distributional issues and an application. Geographical Analysis, 27(4), 286-306. doi:10.1111/j.1538-4632.1995.tb00912.x

Examples

set.seed(1)
p <- cbind(x = runif(60), y = runif(60))
v <- rpois(60, ifelse(p[, 1] > 0.7, 6, 2))
locgi(v, spwt(p, type = "band", d = 0.2, style = "raw"))
#>  [1]  0.23994257 -1.19393804 -0.85693776  4.16902467 -1.51580855  2.62650766
#>  [7]  3.78952137  0.87555456 -0.91284462 -1.74706652 -2.08423675 -0.89182354
#> [13]  1.19393804 -1.51232152  1.27896346 -0.37705262  2.28529782  2.46318889
#> [19] -0.23878761  2.08423675  4.04305111 -1.05904046  0.55717109 -2.22803818
#> [25] -0.07959587 -0.72460663 -1.06343180 -0.56842821  2.08423675 -0.73778305
#> [31] -0.72460663 -0.91284462 -0.72460663 -0.75790427  2.30828021  1.28199634
#> [37]  1.78732733 -1.97494476  2.30828021 -0.56071512  2.09530386  1.19393804
#> [43]  1.03474630  0.30383766 -1.72790811  1.03289627 -1.17365736 -1.62693646
#> [49]  1.44921325  0.78034560 -0.65203187  2.50225827 -1.44605478 -2.08423675
#> [55] -1.51918828 -1.17365736 -1.03474630 -0.91485098 -0.23878761 -0.55738971