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 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.Baddeley@csiro.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 1.25-3 Index]