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)
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