R: Inhomogeneous Cross Type L Function

Lcross.inhom {spatstat} | R Documentation

## 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 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.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

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

`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
        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)

[Package spatstat version 1.54-0 Index]