lctools (version 0.2-10)

spGini: Spatial Gini coefficient

Description

This is the implementation of the spatial decomposition of the Gini coefficient introduced by Rey and Smith (2013). The function calculates the global Gini and the two components of the spatial Gini: the inequality among nearest (geographically) neighbours and the inequality of non-neighbours. Three weighted schemes are currently supported: binary, bi-square and row standardised bi-square.

Usage

spGini(Coords, Bandwidth, x, WType = 'Binary')

Value

Returns a list of five values Gini, gwGini, nsGini, gwGini.frac, nsGini.frac

Gini

Global Gini

gwGini

First component of the spatial Gini: the inequality among nearest (geographically) neighbours

nsGini

Second component of the spatial Gini: the inequality among non-neighbours

gwGini.frac

The fraction of the first component of the spatial Gini

nsGini.frac

The fraction of the second component of the spatial Gini

Arguments

Coords

a numeric matrix or vector or data frame of two columns giving the X,Y coordinates of the observations (data points or geometric / population weighted centroids)

Bandwidth

a positive integer that defines the number of nearest neighbours for the calculation of the weights

x

a numeric vector of a variable

WType

a string giving the weighting scheme used to compute the weights matrix. Options are: "Binary", "Bi-square", "RSBi-square". Default is "Binary".

Binary: weight = 1 for distances less than or equal to the distance of the furthest neighbour (H), 0 otherwise;

Bi-square: weight = (1-(ndist/H)^2)^2 for distances less than or equal to H, 0 otherwise;

RSBi-square: weight = Bi-square weights / sum (Bi-square weights) for each row in the weights matrix

Author

Stamatis Kalogirou <[e-mail]>

References

Rey, S.J., Smith, R. J. (2013) A spatial decomposition of the Gini coefficient, Letters in Spatial and Resource Sciences, 6 (2), pp. 55-70.

Kalogirou, S. (2015) Spatial Analysis: Methodology and Applications with R. [ebook] Athens: Hellenic Academic Libraries Link. ISBN: 978-960-603-285-1 (in Greek). https://repository.kallipos.gr/handle/11419/5029?locale=en

Examples

data(GR.Municipalities)
Coords1<-cbind(GR.Municipalities@data$X, GR.Municipalities@data$Y)
Bandwidth1<-12
x1<-GR.Municipalities@data$Income01
WType1<-'Binary'
spGini(Coords1,Bandwidth1,x1,WType1)