spatstat (version 1.63-3)

Ldot: 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.

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}Li. obtained by the edge corrections named.

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.

See Also

Kdot, Lcross, Lest

Examples

# NOT RUN {
 data(amacrine)
 L <- Ldot(amacrine, "off")
 plot(L)
# }