# localKcross.inhom

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##### Inhomogeneous Multitype K Function

Computes spatially-weighted versions of the the local multitype $$K$$-function or $$L$$-function.

Keywords
spatial, nonparametric
##### Usage
localKcross.inhom(X, from, to,
lambdaFrom=NULL, lambdaTo=NULL,
…, rmax = NULL,
correction = "Ripley", sigma=NULL, varcov=NULL,
lambdaX=NULL, update=TRUE, leaveoneout=TRUE)
localLcross.inhom(X, from, to,
lambdaFrom=NULL, lambdaTo=NULL, …, rmax = NULL)
##### Arguments
X

A point pattern (object of class "ppp").

from

Type of points from which distances should be measured. A single value; one of the possible levels of marks(X), or an integer indicating which level.

to

Type of points to which distances should be measured. A single value; one of the possible levels of marks(X), or an integer indicating which level.

lambdaFrom,lambdaTo

Optional. Values of the estimated intensity function for the points of type from and to, respectively. Each argument should be either a vector giving the intensity values at the required points, a pixel image (object of class "im") giving the intensity values at all locations, a fitted point process model (object of class "ppm") or a function(x,y) which can be evaluated to give the intensity value at any location.

Extra arguments. Ignored if lambda is present. Passed to density.ppp if lambda is omitted.

rmax

Optional. Maximum desired value of the argument $$r$$.

correction

String specifying the edge correction to be applied. Options are "none", "translate", "Ripley", "translation", "isotropic" or "best". Only one correction may be specified.

sigma, varcov

Optional arguments passed to density.ppp to control the kernel smoothing procedure for estimating lambdaFrom and lambdaTo, if they are missing.

lambdaX

Optional. Values of the estimated intensity function for all points of X. Either a vector giving the intensity values at each point of X, a pixel image (object of class "im") giving the intensity values at all locations, a list of pixel images giving the intensity values at all locations for each type of point, or a fitted point process model (object of class "ppm") or a function(x,y) or function(x,y,m) which can be evaluated to give the intensity value at any location.

update

Logical value indicating what to do when lambdaFrom, lambdaTo or lambdaX is a fitted model (class "ppm", "kppm" or "dppm"). If update=TRUE (the default), the model will first be refitted to the data X (using update.ppm or update.kppm) before the fitted intensity is computed. If update=FALSE, the fitted intensity of the model will be computed without re-fitting it to X.

leaveoneout

Logical value (passed to density.ppp or fitted.ppm) specifying whether to use a leave-one-out rule when calculating the intensity.

##### Details

The functions localKcross.inhom and localLcross.inhom are inhomogeneous or weighted versions of the local multitype $$K$$ and $$L$$ functions implemented in localKcross and localLcross.

Given a multitype spatial point pattern X, and two designated types from and to, the local multitype $$K$$ function is defined for each point X[i] that belongs to type from, and is computed by $$K_i(r) = \sqrt{\frac 1 \pi \sum_j \frac{e_{ij}}{\lambda_j}}$$ where the sum is over all points $$j \neq i$$ of type to that lie within a distance $$r$$ of the $$i$$th point, $$\lambda_j$$ is the estimated intensity of the point pattern at the point $$j$$, and $$e_{ij}$$ is an edge correction term (as described in Kest).

The function $$K_i(r)$$ is computed for a range of $$r$$ values for each point $$i$$. The results are stored as a function value table (object of class "fv") with a column of the table containing the function estimates for each point of the pattern X of type from.

The corresponding $$L$$ function $$L_i(r)$$ is computed by applying the transformation $$L(r) = \sqrt{K(r)/(2\pi)}$$.

##### Value

An object of class "fv", see fv.object, which can be plotted directly using plot.fv. Essentially a data frame containing columns

r

the vector of values of the argument $$r$$ at which the function $$K$$ has been estimated

theo

the theoretical value $$K(r) = \pi r^2$$ or $$L(r)=r$$ for a stationary Poisson process

together with columns containing the values of the neighbourhood density function for each point in the pattern of type from. The last two columns contain the r and theo values.

Kinhom, Linhom, localK, localL.

##### Aliases
• localKcross.inhom
• localLcross.inhom
##### Examples
# NOT RUN {
X <- amacrine

# compute all the local L functions
L <- localLcross.inhom(X)

# plot all the local L functions against r
plot(L, main="local L functions for ponderosa", legend=FALSE)

# plot only the local L function for point number 7
plot(L, iso007 ~ r)
# }

Documentation reproduced from package spatstat, version 1.63-0, License: GPL (>= 2)

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