Lcross.inhom
Inhomogeneous Cross Type L Function
For a multitype point pattern, estimate the inhomogeneous version of the cross-type $L$ function.
Usage
Lcross.inhom(X, i, j, ...)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
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). - ...
- 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"(seefv.object).Essentially a data frame containing numeric columns
r the values of the argument $r$ at which the function $L_{ij}(r)$ has been estimated theo the theoretical value of $L_{ij}(r)$ for a marked Poisson process, identically equal to r- together with a column or columns named
"border","bord.modif","iso"and/or"trans", according to the selected edge corrections. These columns contain estimates of the function $L_{ij}(r)$ obtained by the edge corrections named.
References
# 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(lansing, "whiteoak", "maple", lambdaW, lambdaM) # method (2): fit parametric intensity model
fit <- ppm(lansing, ~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, lansing$marks)
L <- Lcross.inhom(lansing, "whiteoak", "maple",
lambda$whiteoak, lambda$maple)
# synthetic example: type A points have intensity 50,
# type B points have intensity 100 * x
lamB <- as.im(function(x,y){50 + 100 * x}, owin())
X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
L <- Lcross.inhom(X, "A", "B",
lambdaI=as.im(50, X$window), lambdaJ=lamB)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.
}
Lcross,
Linhom,
Kcross.inhom