Inhomogeneous Cross Type L Function
For a multitype point pattern, estimate the inhomogeneous version of the cross-type L function.
Lcross.inhom(X, i, j, ..., correction)
X |
The observed point pattern, from which an estimate of the inhomogeneous cross type L function Lij(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 |
j |
The type (mark value)
of the points in |
correction,... |
Other arguments passed to |
All the arguments are passed to Kcross.inhom, which
estimates the inhomogeneous multitype K function
Kij(r) for the point pattern.
The resulting values are then
transformed by taking L(r) = sqrt(K(r)/pi).
An object of class "fv" (see fv.object).
Essentially a data frame containing numeric columns
r |
the values of the argument r at which the function Lij(r) has been estimated |
theo |
the theoretical value of Lij(r)
for a marked Poisson process, identically equal to |
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 Lij(r)
obtained by the edge corrections named.
The arguments i and j are always interpreted as
levels of the factor X$marks. They are converted to character
strings if they are not already character strings.
The value i=1 does not
refer to the first level of the factor.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.
# Lansing Woods data
woods <- lansing
ma <- split(woods)$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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.