spatstat (version 1.16-0)

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, ...)

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

Number or character string identifying the type (mark value) of the points in X from which distances are measured. Defaults to the first level of marks(X).

j

Number or character string identifying the type (mark value) of the points in X to which distances are measured. Defaults to the second level of marks(X).

...

Other arguments passed to Kcross.inhom.

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 interpreted as levels of the factor X$marks. Beware of the usual trap with factors: numerical values are not interpreted in the same way as character values.

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 $L(r) = \sqrt{K(r)/\pi}$.

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
    data(lansing)
    lansing <- lansing[seq(1,lansing$n, by=10)]
    ma <- split(lansing)$maple
    wh <- split(lansing)$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(lansing, "whiteoak", "maple", lambdaW, lambdaM)

    # method (2): fit parametric intensity model
    fit <- ppm(lansing, ~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, lansing$marks)
    L <- Lcross.inhom(lansing, "whiteoak", "maple",
              lambda$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, X$window), lambdaJ=lamB)