Lcross.inhom: Inhomogeneous Cross Type L Function In spatstat: Spatial Point Pattern Analysis, Model-Fitting, Simulation, Tests

Description

For a multitype point pattern, estimate the inhomogeneous version of the cross-type L function.

Usage

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

Arguments

 X The observed point pattern, from which an estimate of the inhomogeneous 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). ... Other arguments passed to Kcross.inhom.

Details

This is a generalisation of the function Lcross to include an adjustment for spatially inhomogeneous intensity, in a manner similar to the function Linhom.

All the arguments are passed to Kcross.inhom, which estimates the inhomogeneous multitype K function Kij(r) for the point pattern. The resulting values are then transformed by taking L(r) = sqrt(K(r)/pi).

Value

An object of class "fv" (see fv.object).

Essentially a data frame containing numeric columns

 r the values of the argument r at which the function Lij(r) has been estimated theo the theoretical value of Lij(r) for a marked Poisson process, identically equal to r

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

Warnings

The arguments i and j are always interpreted as levels of the factor X\$marks. They are converted to character strings if they are not already character strings. The value i=1 does not refer to the first level of the factor.

and \rolf

References

Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.