R: Inhomogeneous Multitype K Function

localKcross.inhom {spatstat} | R Documentation

## Inhomogeneous Multitype K Function

### Description

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

### 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( (1/pi) * sum[j] e[i,j]/lambda[j])

where the sum is over all points j != i of type `to` that lie within a distance r of the ith point, λ[j] is the estimated intensity of the point pattern at the point j, and e[i,j] 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.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

### See Also

`Kinhom`, `Linhom`, `localK`, `localL`.

### Examples

      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)

[Package spatstat version 1.63-3 Index]