R: Multitype L-function (cross-type)

Lcross {spatstat.core} | R Documentation

## Multitype L-function (cross-type)

### Description

Calculates an estimate of the cross-type L-function for a multitype point pattern.

### Usage

      Lcross(X, i, j, ..., from, to, correction)

### Arguments

`X` | The observed point pattern, from which an estimate of the 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,...` | Arguments passed to `Kcross`.
`from,to` | An alternative way to specify `i` and `j` respectively.

### Details

The cross-type L-function is a transformation of the cross-type K-function,

Lij(r) = sqrt(Kij(r)/pi)

where Kij(r) is the cross-type K-function from type `i` to type `j`. See `Kcross` for information about the cross-type K-function.

The command `Lcross` first calls `Kcross` to compute the estimate of the cross-type K-function, and then applies the square root transformation.

For a marked point pattern in which the points of type `i` are independent of the points of type `j`, the theoretical value of the L-function is Lij(r) = r. The square root also has the effect of stabilising the variance of the estimator, so that Lij is more appropriate for use in simulation envelopes and hypothesis tests.

### Value

An object of class `"fv"`, see `fv.object`, which can be plotted directly using `plot.fv`.

Essentially a data frame containing columns

`r` | the vector of values of the argument r at which the function Lij has been estimated
`theo` | the theoretical value Lij(r) = r for a stationary Poisson process

together with columns named `"border"`, `"bord.modif"`, `"iso"` and/or `"trans"`, according to the selected edge corrections. These columns contain estimates of the function Lij obtained by the edge corrections named.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

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

### See Also

`Kcross`, `Ldot`, `Lest`

### Examples

     data(amacrine)
     L <- Lcross(amacrine, "off", "on")
     plot(L)

[Package spatstat.core version 1.65-5 Index]