lctools (version 0.2-10)

w.matrix: Weights Matrix based on a number of nearest neighbours or a fixed distance

Description

This function constructs an n by n weights matrix for a geography with n geographical elements (e.g. points or polygons) using a number of nearest neighbours or a fixed distance.

Usage

w.matrix(Coords, Bandwidth, WType = "Binary", family = "adaptive")

Value

A matrix of weights

Arguments

Coords

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

Bandwidth

either a positive integer that defines the number of nearest neighbours for the calculation of the weights of an adaptive kernel (family = 'adaptive') or a fixed distance in meters for a fixed kernel (family = 'fixed').

WType

a string giving the weighting function used to compute the weights matrix. Options are: "Binary", "Bi-square", and "RSBi-square". The default value 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

family

a string giving the weighting scheme used to compute the weights matrix. Options are: "adaptive" and "fixed". The default value is "adaptive".

adaptive: the number of nearest neighbours (integer).

fixed: a fixed distance around each observation's location (in meters).

Author

Stamatis Kalogirou <[e-mail]>

References

Kalogirou, S. (2003) The Statistical Analysis and Modelling of Internal Migration Flows within England and Wales, PhD Thesis, School of Geography, Politics and Sociology, University of Newcastle upon Tyne, UK. https://theses.ncl.ac.uk/jspui/handle/10443/204

See Also

moransI.w, spGini.w

Examples

data(GR.Municipalities)
attr <- GR.Municipalities@data

#adaptive kernel
w.adapt <- w.matrix(cbind(attr$X, attr$Y),6, WType='Binary', family='adaptive')

#fixed kernel
w.fixed <- w.matrix(cbind(attr$X, attr$Y), 50000, WType='Binary', family='fixed')