Lcross.inhom: Inhomogeneous Cross Type L Function

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

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 L_{ij}(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 K_{ij}(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 L_{ij}(r) has been estimated
theo	the theoretical value of L_{ij}(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 L_{ij}(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)

\adrian

and \rolf

References

\Moller

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

See Also

Lcross, Linhom, Kcross.inhom

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
    if(require("spatstat.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.explore documentation built on Oct. 22, 2024, 9:07 a.m.