Lcross.inhom
Inhomogeneous Cross Type L Function
For a multitype point pattern, estimate the inhomogeneous version of the cross-type \(L\) function.
- Keywords
- spatial, nonparametric
Usage
Lcross.inhom(X, i, j, …, correction)
Arguments
- X
The observed point pattern, from which an estimate of the inhomogeneous 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
X
from 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
X
to 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,…
Other arguments passed to
Kcross.inhom
.
Details
This is a generalisation of the function Lcross
to include an adjustment for spatially inhomogeneous intensity,
in a manner similar to the function Linhom
.
All the arguments are passed to Kcross.inhom
, which
estimates the inhomogeneous multitype K function
\(K_{ij}(r)\) for the point pattern.
The resulting values are then
transformed by taking \(L(r) = \sqrt{K(r)/\pi}\).
Value
An object of class "fv"
(see fv.object
).
Essentially a data frame containing numeric columns
the values of the argument \(r\) at which the function \(L_{ij}(r)\) has been estimated
the theoretical value of \(L_{ij}(r)\)
for a marked Poisson process, identically equal to r
Warnings
The arguments i
and j
are always interpreted as
levels of the factor X$marks
. They are converted to character
strings if they are not already character strings.
The value i=1
does not
refer to the first level of the factor.
References
Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.
See Also
Examples
# NOT RUN {
# Lansing Woods data
woods <- lansing
# }
# NOT RUN {
ma <- split(woods)$maple
wh <- split(woods)$whiteoak
# method (1): estimate intensities by nonparametric smoothing
lambdaM <- density.ppp(ma, sigma=0.15, at="points")
lambdaW <- density.ppp(wh, sigma=0.15, at="points")
L <- Lcross.inhom(woods, "whiteoak", "maple", lambdaW, lambdaM)
# method (2): fit parametric intensity model
fit <- ppm(woods ~marks * polynom(x,y,2))
# evaluate fitted intensities at data points
# (these are the intensities of the sub-processes of each type)
inten <- fitted(fit, dataonly=TRUE)
# split according to types of points
lambda <- split(inten, marks(woods))
L <- Lcross.inhom(woods, "whiteoak", "maple",
lambda$whiteoak, lambda$maple)
# synthetic example: type A points have intensity 50,
# type B points have intensity 100 * x
lamB <- as.im(function(x,y){50 + 100 * x}, owin())
X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
L <- Lcross.inhom(X, "A", "B",
lambdaI=as.im(50, Window(X)), lambdaJ=lamB)
# }