# 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.

Keywords
spatial, nonparametric
##### 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

r

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

theo

the 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)Lij(r) obtained by the edge corrections named.

The arguments i and j are always interpreted as levels of the factor X$marks. They are converted to character strings if they are not already character strings. The value i=1 does not refer to the first level of the factor. ##### References Moller, J. and Waagepetersen, R. Statistical Inference and Simulation for Spatial Point Processes Chapman and Hall/CRC Boca Raton, 2003. ##### See Also Lcross, Linhom, Kcross.inhom ##### Aliases • Lcross.inhom ##### Examples # NOT RUN { # Lansing Woods data woods <- lansing # } # NOT RUN { ma <- split(woods)$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)
# }

Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)

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