spatstat (version 1.46-1)

Lcross: 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, ..., from, to)

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

The type (mark value) of the points in X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).

j

The type (mark value) of the points in X to which distances are measured. A character string (or something that will be converted to a character string). Defaults to the second level of marks(X).

...

Arguments passed to Kcross.

from,to

An alternative way to specify i and j respectively.

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.

Details

The cross-type L-function is a transformation of the cross-type K-function, $$L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}$$ 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.

See Also

Kcross, Ldot, Lest

Examples

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