R: Multitype L-function (i-to-any)

Ldot {spatstat.core} | R Documentation

## Multitype L-function (i-to-any)

### Description

Calculates an estimate of the multitype L-function (from type `i` to any type) for a multitype point pattern.

### Usage

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

### Arguments

`X` | The observed point pattern, from which an estimate of the dot-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)`.
`correction,...` | Arguments passed to `Kdot`.
`from` | An alternative way to specify `i`.

### Details

This command computes

Li.(r) = sqrt(Ki.(r)/pi)

where Ki.(r) is the multitype K-function from points of type `i` to points of any type. See `Kdot` for information about Ki.(r).

The command `Ldot` first calls `Kdot` to compute the estimate of the `i`-to-any K-function, and then applies the square root transformation.

For a marked Poisson point process, the theoretical value of the L-function is Li.(r) = r. The square root also has the effect of stabilising the variance of the estimator, so that Li. 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 Li. has been estimated
`theo` | the theoretical value Li.(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 Li. 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

`Kdot`, `Lcross`, `Lest`

### Examples

     data(amacrine)
     L <- Ldot(amacrine, "off")
     plot(L)

[Package spatstat.core version 2.0-0 Index]