# Lcross.inhom

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##### 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 X from which distances are measured. A character string (or something that will be converted to a character string). Defaults to the first level of marks(X).
j
The type (mark value) of the points in X to which distances are measured. A character string (or something that will be converted to a character string). Defaults to the second level of marks(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" (see fv.object).

Essentially a data frame containing numeric columns

• rthe values of the argument $r$ at which the function $L_{ij}(r)$ has been estimated
• theothe 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

latex{Mller{Moller}, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003. }

Warnings
{ The arguments i and j are always interpreted as levels of the factor X$marks. They are converted to character strings if they are not already character strings. The value i=1 does not refer to the first level of the factor. } Lcross, Linhom, Kcross.inhom # Lansing Woods data data(lansing) lansing <- lansing[seq(1,lansing$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)

[object Object],[object Object],[object Object] spatial nonparametric

##### Aliases
• Lcross.inhom
Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)

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