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Lcross.inhom

Inhomogeneous Cross Type L Function


Description

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

Usage

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

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).

correction,...

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.

Author(s)

and Rolf Turner r.turner@auckland.ac.nz

References

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

See Also

Examples

# Lansing Woods data
    woods <- lansing
    
    ma <- split(woods)$maple
    wh <- split(woods)$whiteoak

    # method (1): estimate intensities by nonparametric smoothing
    lambdaM <- density.ppp(ma, sigma=0.15, at="points")
    lambdaW <- density.ppp(wh, sigma=0.15, at="points")
    L <- Lcross.inhom(woods, "whiteoak", "maple", lambdaW, lambdaM)

    # method (2): fit parametric intensity model
    fit <- ppm(woods ~marks * polynom(x,y,2))
    # evaluate fitted intensities at data points
    # (these are the intensities of the sub-processes of each type)
    inten <- fitted(fit, dataonly=TRUE)
    # split according to types of points
    lambda <- split(inten, marks(woods))
    L <- Lcross.inhom(woods, "whiteoak", "maple",
              lambda$whiteoak, lambda$maple)
    
    # synthetic example: type A points have intensity 50,
    #                    type B points have intensity 100 * x
    lamB <- as.im(function(x,y){50 + 100 * x}, owin())
    X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
    L <- Lcross.inhom(X, "A", "B",
        lambdaI=as.im(50, Window(X)), lambdaJ=lamB)

spatstat.core

Core Functionality of the 'spatstat' Family

v2.1-2
GPL (>= 2)
Authors
Adrian Baddeley [aut, cre], Rolf Turner [aut], Ege Rubak [aut], Kasper Klitgaard Berthelsen [ctb], Achmad Choiruddin [ctb], Jean-Francois Coeurjolly [ctb], Ottmar Cronie [ctb], Tilman Davies [ctb], Julian Gilbey [ctb], Yongtao Guan [ctb], Ute Hahn [ctb], Kassel Hingee [ctb], Abdollah Jalilian [ctb], Marie-Colette van Lieshout [ctb], Greg McSwiggan [ctb], Tuomas Rajala [ctb], Suman Rakshit [ctb], Dominic Schuhmacher [ctb], Rasmus Plenge Waagepetersen [ctb], Hangsheng Wang [ctb]
Initial release
2021-04-17

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