R: Inhomogeneous Neighbourhood Density Function

localKinhom {spatstat.core} | R Documentation

## Inhomogeneous Neighbourhood Density Function

### Description

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

### Usage

      localKinhom(X, lambda, ..., rmax = NULL,
                  correction = "Ripley", verbose = TRUE, rvalue=NULL,
                  sigma = NULL, varcov = NULL, update=TRUE, leaveoneout=TRUE)
      localLinhom(X, lambda, ..., rmax = NULL,
                  correction = "Ripley", verbose = TRUE, rvalue=NULL,
                  sigma = NULL, varcov = NULL, update=TRUE, leaveoneout=TRUE)

### Arguments

`X` | A point pattern (object of class `"ppp"`).
`lambda` | Optional. Values of the estimated intensity function. Either a vector giving the intensity values at the points of the pattern `X`, a pixel image (object of class `"im"`) giving the intensity values at all locations, a fitted point process model (object of class `"ppm"` or `"kppm"` or `"dppm"`) 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.
`verbose` | Logical flag indicating whether to print progress reports during the calculation.
`rvalue` | Optional. A single value of the distance argument r at which the function L or K should be computed.
`sigma, varcov` | Optional arguments passed to `density.ppp` to control the kernel smoothing procedure for estimating `lambda`, if `lambda` is missing.
`leaveoneout` | Logical value (passed to `density.ppp` or `fitted.ppm`) specifying whether to use a leave-one-out rule when calculating the intensity.
`update` | Logical value indicating what to do when `lambda` 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`.

### Details

The functions `localKinhom` and `localLinhom` are inhomogeneous or weighted versions of the neighbourhood density function implemented in `localK` and `localL`.

Given a spatial point pattern `X`, the inhomogeneous neighbourhood density function L[i](r) associated with the ith point in `X` is computed by

L[i](r) = sqrt( (1/pi) * sum[j] e[i,j]/lambda[j])

where the sum is over all points j != i 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 value of L[i](r) can also be interpreted as one of the summands that contributes to the global estimate of the inhomogeneous L function (see `Linhom`).

By default, the function L[i](r) or 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`.

Alternatively, if the argument `rvalue` is given, and it is a single number, then the function will only be computed for this value of r, and the results will be returned as a numeric vector, with one entry of the vector for each point of the pattern `X`.

### Value

If `rvalue` is given, the result is a numeric vector of length equal to the number of points in the point pattern.

If `rvalue` is absent, the result is 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. Column `i` corresponds to the `i`th point. The last two columns contain the `r` and `theo` values.

### Author(s)

Mike Kuhn, Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

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

### Examples

      data(ponderosa)
      X <- ponderosa

      # compute all the local L functions
      L <- localLinhom(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)

      # compute the values of L(r) for r = 12 metres
      L12 <- localL(X, rvalue=12)

[Package spatstat.core version 2.0-0 Index]