localKcross.inhom

From spatstat v1.63-0 by Adrian Baddeley

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

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.

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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