Lcross
Multitype L-function (cross-type)
Calculates an estimate of the cross-type L-function for a multitype point pattern.
- Keywords
- spatial, nonparametric
Usage
Lcross(X, i, j, ..., from, to, correction)Arguments
- X
The observed point pattern, from which an estimate of the cross-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
Xfrom which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level ofmarks(X).- j
The type (mark value) of the points in
Xto which distances are measured. A character string (or something that will be converted to a character string). Defaults to the second level ofmarks(X).- correction,…
Arguments passed to
Kcross.- from,to
An alternative way to specify
iandjrespectively.
Details
The cross-type L-function is a transformation of the cross-type K-function,
$$L_{ij}(r) = \sqrt{\frac{K_{ij}(r)}{\pi}}$$
where \(K_{ij}(r)\) 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
\(L_{ij}(r) = r\).
The square root also has the effect of stabilising
the variance of the estimator, so that \(L_{ij}\) 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
the vector of values of the argument \(r\) at which the function \(L_{ij}\) has been estimated
the theoretical value \(L_{ij}(r) = r\) for a stationary Poisson process
See Also
Examples
# NOT RUN {
data(amacrine)
L <- Lcross(amacrine, "off", "on")
plot(L)
# }