Ldot {spatstat.explore}

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.

Author(s)

Adrian Baddeley [e-mail] and Rolf Turner [e-mail]

See Also

Kdot, Lcross, Lest

Examples

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