Ldot.inhom
Inhomogeneous Multitype L Dot Function
For a multitype point pattern, estimate the inhomogeneous version of the dot $L$ function.
- Keywords
- spatial, nonparametric
Usage
Ldot.inhom(X, i, ...)
Arguments
- X
- The observed point pattern, from which an estimate of the inhomogeneous cross type $L$ function $L_{i\bullet}(r)$ 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 ofmarks(X)
. - ...
- Other arguments passed to
Kdot.inhom
.
Details
This a generalisation of the function Ldot
to include an adjustment for spatially inhomogeneous intensity,
in a manner similar to the function Linhom
.
All the arguments are passed to Kdot.inhom
, which
estimates the inhomogeneous multitype K function
$K_{i\bullet}(r)$ 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 $L_{i\bullet}(r)$ has been estimated theo the theoretical value of $L_{i\bullet}(r)$ for a marked Poisson process, identical 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 $L_{i\bullet}(r)$ obtained by the edge corrections named.
Warnings
The argument i
is interpreted as a
level of the factor X$marks
. Beware of the usual
trap with factors: numerical values are not
interpreted in the same way as character values.
References
Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003.
See Also
Examples
# Lansing Woods data
data(lansing)
lansing <- lansing[seq(1,lansing$n, by=10)]
ma <- split(lansing)$maple
lg <- unmark(lansing)
# Estimate intensities by nonparametric smoothing
lambdaM <- density.ppp(ma, sigma=0.15, at="points")
lambdadot <- density.ppp(lg, sigma=0.15, at="points")
L <- Ldot.inhom(lansing, "maple", lambdaI=lambdaM,
lambdadot=lambdadot)
# synthetic example: type A points have intensity 50,
# type B points have intensity 50 + 100 * x
lamB <- as.im(function(x,y){50 + 100 * x}, owin())
lamdot <- as.im(function(x,y) { 100 + 100 * x}, owin())
X <- superimpose(A=runifpoispp(50), B=rpoispp(lamB))
L <- Ldot.inhom(X, "B", lambdaI=lamB, lambdadot=lamdot)