Lcross {spatstat}R Documentation

Multitype L-function (cross-type)

Description

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

Usage

  Lcross(X, i, j, ...)

Arguments

X The observed point pattern, from which an estimate of the cross-type L function Lij(r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.
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 Kcross.

Details

The cross-type L-function is a transformation of the cross-type K-function,

Lij(r) = sqrt(Kij(r)/pi)

where Kij(r) is the cross-type K-function from type i to type j. See Kcross for information about the cross-type K-function.

The command Lcross first calls Kcross to compute the estimate of the cross-type K-function, and then applies the square root transformation.

For a marked point pattern in which the points of type i are independent of the points of type j, the theoretical value of the L-function is Lij(r) = r. The square root also has the effect of stabilising the variance of the estimator, so that L_{ij}{Lij} is more appropriate for use in simulation envelopes and hypothesis tests.

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 Lij has been estimated
theo the theoretical value Lij(r) = r for a stationary Poisson process

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

Author(s)

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

See Also

Kcross, Ldot, Lest

Examples

 data(amacrine)
 L <- Lcross(amacrine, "off", "on")
 plot(L)

[Package spatstat version 1.13-3 Index]