Linhom {spatstat.explore}R Documentation

Inhomogeneous L-function

Description

Calculates an estimate of the inhomogeneous version of the LL-function (Besag's transformation of Ripley's KK-function) for a spatial point pattern.

Usage

  Linhom(X, ..., correction)

Arguments

X

The observed point pattern, from which an estimate of L(r)L(r) will be computed. An object of class "ppp", or data in any format acceptable to as.ppp().

correction, ...

Other arguments passed to Kinhom to control the estimation procedure.

Details

This command computes an estimate of the inhomogeneous version of the LL-function for a spatial point pattern.

The original LL-function is a transformation (proposed by Besag) of Ripley's KK-function,

L(r)=K(r)πL(r) = \sqrt{\frac{K(r)}{\pi}}

where K(r)K(r) is the Ripley KK-function of a spatially homogeneous point pattern, estimated by Kest.

The inhomogeneous LL-function is the corresponding transformation of the inhomogeneous KK-function, estimated by Kinhom. It is appropriate when the point pattern clearly does not have a homogeneous intensity of points. It was proposed by Baddeley, Moller and Waagepetersen (2000).

The command Linhom first calls Kinhom to compute the estimate of the inhomogeneous K-function, and then applies the square root transformation.

For a Poisson point pattern (homogeneous or inhomogeneous), the theoretical value of the inhomogeneous LL-function is L(r)=rL(r) = r. The square root also has the effect of stabilising the variance of the estimator, so that LL 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 rr at which the function LL has been estimated

theo

the theoretical value L(r)=rL(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 L(r)L(r) obtained by the edge corrections named.

Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner rolfturner@posteo.net

References

Baddeley, A., Moller, J. and Waagepetersen, R. (2000) Non- and semiparametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica 54, 329–350.

See Also

Kest, Lest, Kinhom, pcf

Examples

 X <- japanesepines
 L <- Linhom(X, sigma=0.1)
 plot(L, main="Inhomogeneous L function for Japanese Pines")

[Package spatstat.explore version 3.3-1 Index]