R: Inhomogeneous Multitype L Dot Function

Ldot.inhom {spatstat} | R Documentation

## Inhomogeneous Multitype L Dot Function

### Description

For a multitype point pattern, estimate the inhomogeneous version of the dot L function.

### Usage

    Ldot.inhom(X, i, ..., correction)

### Arguments

`X` | The observed point pattern, from which an estimate of the inhomogeneous cross type L function Li.(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)`.
`correction,...` | Other arguments passed to `Kdot.inhom`.

### Details

This a generalisation of the function `Ldot` to include an adjustment for spatially inhomogeneous intensity, in a manner similar to the function `Linhom`.

All the arguments are passed to `Kdot.inhom`, which estimates the inhomogeneous multitype K function Ki.(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 Li.(r) has been estimated
`theo` | the theoretical value of Li.(r) for a marked Poisson process, identical 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 Li.(r) obtained by the edge corrections named.

### Warnings

The argument `i` is interpreted as a level of the factor `X$marks`. It is converted to a character string if it is not already a character string. The value `i=1` does not refer to the first level of the factor.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk

### References

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

### See Also

`Ldot`, `Linhom`, `Kdot.inhom`, `Lcross.inhom`.

### Examples

        # Lansing Woods data
        lan <- lansing
        lan <- lan[seq(1,npoints(lan), by=10)]
        ma <- split(lan)$maple
        lg <- unmark(lan)

        # Estimate intensities by nonparametric smoothing
        lambdaM <- density.ppp(ma, sigma=0.15, at="points")
        lambdadot <- density.ppp(lg, sigma=0.15, at="points")
        L <- Ldot.inhom(lan, "maple", lambdaI=lambdaM,
                                      lambdadot=lambdadot)

        # synthetic example: type A points have intensity 50,
        #                    type B points have intensity 50 + 100 * x
        lamB <- as.im(function(x,y){50 + 100 * x}, owin())
        lamdot <- as.im(function(x,y) { 100 + 100 * x}, owin())
        X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
        L <- Ldot.inhom(X, "B",  lambdaI=lamB,     lambdadot=lamdot)

[Package spatstat version 1.63-3 Index]