pcfcross {spatstat}R Documentation

Multitype pair correlation function (cross-type)

Description

Calculates an estimate of the cross-type pair correlation function for a multitype point pattern.

Usage

  pcfcross(X, i, j, ...)

Arguments

X

The observed point pattern, from which an estimate of the cross-type pair correlation function g[i,j](r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor).

i

Number or character string identifying the type (mark value) of the points in X from which distances are measured.

j

Number or character string identifying the type (mark value) of the points in X to which distances are measured.

...

Arguments passed to pcf.ppp.

Details

The cross-type pair correlation function is a generalisation of the pair correlation function pcf to multitype point patterns.

For two locations x and y separated by a distance r, the probability p(r) of finding a point of type i at location x and a point of type j at location y is

p(r) = lambda[i] * lambda[j] * g[i,j](r) dx dy

where lambda[i] is the intensity of the points of type i. For a completely random Poisson marked point process, p(r) = lambda[i] * lambda[j] so g[i,j](r) = 1. Indeed for any marked point pattern in which the points of type i are independent of the points of type j, the theoretical value of the cross-type pair correlation is g[i,j](r) = 1.

For a stationary multitype point process, the cross-type pair correlation function between marks i and j is formally defined as

g(r) = K[i,j]'(r)/ ( 2 * pi * r)

where K[i,j]'(r) is the derivative of the cross-type K function K[i,j](r). of the point process. See Kest for information about K(r).

The command pcfcross computes a kernel estimate of the cross-type pair correlation function between marks i and j. It uses pcf.ppp to compute kernel estimates of the pair correlation functions for several unmarked point patterns, and uses the bilinear properties of second moments to obtain the cross-type pair correlation.

See pcf.ppp for a list of arguments that control the kernel estimation.

The companion function pcfdot computes the corresponding analogue of Kdot.

Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv.

Essentially a data frame containing columns

r

the vector of values of the argument r at which the function g[i,j] has been estimated

theo

the theoretical value g[i,j](r) = r for independent marks.

together with columns named "border", "bord.modif", "iso" and/or "trans", according to the selected edge corrections. These columns contain estimates of the function g[i,j] obtained by the edge corrections named.

Author(s)

Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz

See Also

Mark connection function markconnect.

Multitype pair correlation pcfdot.

Pair correlation pcf,pcf.ppp.

Kcross

Examples

 data(amacrine)
 p <- pcfcross(amacrine, "off", "on")
 p <- pcfcross(amacrine, "off", "on", stoyan=0.1)
 plot(p)

[Package spatstat version 1.25-3 Index]