localmoran: Local Moran's I statistic

Description

The local spatial statistic Moran's I is calculated for each zone based on the spatial weights object used. The values returned include a Z-value, and may be used as a diagnostic tool. The statistic is: $$I_i = \frac{(x_i-\bar{x})}{{\sum_{k=1}^{n}(x_k-\bar{x})^2}/n}{\sum_{j=1}^{n}w_{ij}(x_j-\bar{x})}$$, and its expectation and variance are given in Anselin (1995).

Usage

localmoran(x, listw, zero.policy=FALSE)

Arguments

a numeric vector the same length as the neighbours list in listw

listw

a listw object created for example by nb2listw

zero.policy

if TRUE assign zero to the lagged value of zones without neighbours, if FALSE assign NA

Value

Iilocal moran statistic
E.Iiexpectation of local moran statistic
Var.Iivariance of local moran statistic
Z.Iistandard deviate of local moran statistic

References

Anselin, L. 1995. Local indicators of spatial association, Geographical Analysis, 27, 93--115; Getis, A. and Ord, J. K. 1996 Local spatial statistics: an overview. In P. Longley and M. Batty (eds) Spatial analysis: modelling in a GIS environment (Cambridge: Geoinformation International), 261--277.

Examples

Run this code

data(afcon)
oid <- order(afcon$id)
resG <- localG(afcon$totcon, nb2listw(include.self(paper.nb)))
print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2)
resI <- localmoran(afcon$totcon, nb2listw(paper.nb))
print(data.frame(resI[oid,], row.names=afcon$name[oid]), digits=2)