localenv: Local Population Composition

Description

localenv calculates the local population composition at each data point from a matrix of coordinates, or an object of class Spatial or ppp.

Usage

localenv(x, data, power = 2, useExp = TRUE, maxdist, sprel, 
         tol = .Machine$double.eps)

Arguments

a numeric matrix or data frame with coordinates (each row is a point), or an object of class Spatial or ppp.

data

an object of class matrix, or one that can be coerced to that class. The number of rows in data should equal the number of points in x, and the number of columns should be greater than one (at least two popul

power

a numeric value that determines the change rate of a distance weight function. If zero, all data points have the same weight regardless of the distance. Typically 1-5.

useExp

logical. If FALSE, use a simple inverse distance function instead of a negative exponential function. See Details.

maxdist

an optional numeric value specifying a search radius for the construction of each local environment. Must be a positive value, or zero.

sprel

an optional object of class dist or nb. See Details.

tol

a small, positive non-zero value. If useExp is FALSE, this value will be added to the denominator to avoid the divide-by-zero error.

Value

An object of SegLocal-class.

Details

At each data point in x, localenv calculates the weighted average of the populations of all points that are within a search radius maxdist. The output from this function is an essential component to compute the spatial segregation measures. By default, the weight of each point is calculated from a negative exponential function, which is defined as: $$w(d) = e^{-d \times power}$$ where d is the Euclidean distance between two points. If useExp is FALSE, a simple inverse distance function is used to calculate the weight of each point: $$w(d) = \frac{1}{(d + error)^{power}}$$ If maxdist is not provided (default), all data points in the study area are used for the construction of each local environment. It is recommended to specify this parameter to speed up the calculation process. If a distance measure other than the Euclidean distance is required to represent spatial proximity between the points, users can provide an object of class dist, which contains the distances between all pairs of the points, through an optional argument sprel. One convenient way of obtaining such information may be the use of the function dist, which offers a variety of distance measures, such as Manhattan, Canberra, and Minkowski. Or alternatively, one can supply an object of class nb to use a k-nearest neighbour averaging or polygon contiguity.

Examples

Run this code

# uses the idealised landscapes in 'segdata'
data(segdata)
grd <- GridTopology(cellcentre.offset=c(0.5,0.5),
                    cellsize=c(1,1), cells.dim=c(10,10))
grd.sp <- as.SpatialPolygons.GridTopology(grd)

# complete segregation:
# negative exponential function of distance
xx1 <- localenv(grd.sp, data = segdata[,1:2])
spplot(xx1, main = "Negative exponential")

# inverse distance
xx2 <- localenv(grd.sp, data = segdata[,1:2], useExp = FALSE)
spplot(xx2, main = "Inverse distance")

# inverse distance with p = 0, i.e., weight all points equally
xx3 <- localenv(grd.sp, data = segdata[,1:2], useExp = FALSE, power = 0)
spplot(xx3, main = "Inverse distance with p = 0")

# checkerboard pattern:
# negative exponential function with different p values
vv1 <- localenv(grd.sp, data = segdata[,5:6], power = 1)
spplot(vv1, main = "Negative exponetial with p = 1")

vv2 <- localenv(grd.sp, data = segdata[,5:6])
spplot(vv2, main = "Negative exponetial with p = 2")

vv3 <- localenv(grd.sp, data = segdata[,5:6], power = 3)
spplot(vv3, main = "Negative exponetial with p = 3")