| Lcross.inhom {spatstat} | R Documentation |
For a multitype point pattern, estimate the inhomogeneous version of the cross-type L function.
Lcross.inhom(X, i, j, ...)
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 |
Number or character string identifying the type (mark value)
of the points in X from which distances are measured.
Defaults to the first level of marks(X).
|
j |
Number or character string identifying the type (mark value)
of the points in X to which distances are measured.
Defaults to the second level of marks(X).
|
... |
Other arguments passed to Kcross.inhom.
|
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
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 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 Lij(r)
obtained by the edge corrections named.
The arguments i and j are interpreted as
levels of the factor X$marks. Beware of the usual
trap with factors: numerical values are not
interpreted in the same way as character values.
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.
# Lansing Woods data
data(lansing)
lansing <- lansing[seq(1,lansing$n, by=10)]
ma <- split(lansing)$maple
wh <- split(lansing)$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(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)