The general G of Getis and Ord

The global concentration statistic of Getis and Ord (1992) for non-negative values: G = sum_ij w_ij x_i x_j / sum_{i != j} x_i x_j, its expectation S0 / (n (n - 1)) and variance under randomisation, the z statistic, its upper normal tail (high values near high values) and, with nsim > 0, a permutation p-value. Unlike Moran's I and Geary's C it tells high-value clusters from low-value ones. Its expectation under randomisation is proved in Lean: see proof("gorg").

Usage

gorg(x, w, nsim = 0, seed = NULL)

Arguments

x

The values: finite numbers from 0, at least two positive.

w

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

nsim

The number of permutations: a whole number from 0.

seed

NULL to draw the simulations' seed from R's generator (so set.seed() fixes them), or one whole number from 0.

Value

A named numeric vector: g, e, v, z, p and pperm ((1 + #{G* >= G}) / (nsim + 1)).

References

Getis, A. and Ord, J. K. (1992). The analysis of spatial association by use of distance statistics. Geographical Analysis, 24(3), 189-206. doi:10.1111/j.1538-4632.1992.tb00261.x

Examples

set.seed(1)
p <- cbind(x = runif(50), y = runif(50))
gorg(exp(3 * p[, 1]), spwt(p, type = "band", d = 0.2, style = "raw"))
#>            g            e            v            z            p        pperm 
#> 1.663958e-01 1.167347e-01 1.514881e-04 4.034852e+00 2.731842e-05          NaN