Ldot: Multitype L-function (i-to-any)
In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Ldot	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 `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`	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

L_{i\bullet}(r) = \sqrt{\frac{K_{i\bullet}(r)}{\pi}}

where K_{i\bullet}(r) is the multitype K-function from points of type i to points of any type. See Kdot for information about K_{i\bullet}(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 L_{i\bullet}(r) = r. The square root also has the effect of stabilising the variance of the estimator, so that L_{i\bullet} 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 `L_{i\bullet}` has been estimated
`theo`	the theoretical value `L_{i\bullet}(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 L_{i\bullet} obtained by the edge corrections named.