Calculates an estimate of the cross-type L-function for a multitype point pattern.
Lcross(X, i, j, ..., from, to, correction)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
together with columns named
"border", "bord.modif",
"iso" and/or "trans",
according to the selected edge corrections. These columns contain
estimates of the function \(L_{ij}\) obtained by the edge corrections
named.
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.
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).
The type (mark value)
of the points in X to which distances are measured.
A character string (or something that will be
converted to a character string).
Defaults to the second level of marks(X).
Arguments passed to Kcross.
An alternative way to specify i and j respectively.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au and Rolf Turner r.turner@auckland.ac.nz
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.
Kcross,
Ldot,
Lest
L <- Lcross(amacrine, "off", "on")
plot(L)
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