R: Inhomogeneous Multitype Pair Correlation Function...

pcfcross.inhom {spatstat.core} | R Documentation

## Inhomogeneous Multitype Pair Correlation Function (Cross-Type)

### Description

Estimates the inhomogeneous cross-type pair correlation function for a multitype point pattern.

### Usage

    pcfcross.inhom(X, i, j, lambdaI = NULL, lambdaJ = NULL, ...,
                   r = NULL, breaks = NULL,
                   kernel="epanechnikov", bw=NULL, stoyan=0.15,
                   correction = c("isotropic", "Ripley", "translate"),
                   sigma = NULL, varcov = NULL)

### Arguments

`X` | The observed point pattern, from which an estimate of the inhomogeneous cross-type pair correlation function g[i,j](r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor).
`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)`.
`lambdaI` | Optional. Values of the estimated intensity function of the points of type `i`. Either a vector giving the intensity values at the points of type `i`, a pixel image (object of class `"im"`) giving the intensity values at all locations, or a `function(x,y)` which can be evaluated to give the intensity value at any location.
`lambdaJ` | Optional. Values of the estimated intensity function of the points of type `j`. A numeric vector, pixel image or `function(x,y)`.
`r` | Vector of values for the argument r at which g[i,j](r) should be evaluated. There is a sensible default.
`breaks` | This argument is for internal use only.
`kernel` | Choice of smoothing kernel, passed to `density.default`.
`bw` | Bandwidth for smoothing kernel, passed to `density.default`.
`...` | Other arguments passed to the kernel density estimation function `density.default`.
`stoyan` | Bandwidth coefficient; see Details.
`correction` | Choice of edge correction.
`sigma,varcov` | Optional arguments passed to `density.ppp` to control the smoothing bandwidth, when `lambdaI` or `lambdaJ` is estimated by kernel smoothing.

### Details

The inhomogeneous cross-type pair correlation function g[i,j](r) is a summary of the dependence between two types of points in a multitype spatial point process that does not have a uniform density of points.

The best intuitive interpretation is the following: the probability p(r) of finding two points, of types i and j respectively, at locations x and y separated by a distance r is equal to

p(r) = lambda[i](x) * lambda[j](y) * g(r) dx dy

where lambda[i] is the intensity function of the process of points of type i. For a multitype Poisson point process, this probability is p(r) = lambda[i](x) * lambda[j](y) so g[i,j](r) = 1.

The command `pcfcross.inhom` estimates the inhomogeneous pair correlation using a modified version of the algorithm in `pcf.ppp`.

If the arguments `lambdaI` and `lambdaJ` are missing or null, they are estimated from `X` by kernel smoothing using a leave-one-out estimator.

### Value

A function value table (object of class `"fv"`). Essentially a data frame containing the variables

`r` | the vector of values of the argument r at which the inhomogeneous cross-type pair correlation function g[i,j](r) has been estimated
`theo` | vector of values equal to 1, the theoretical value of g[i,j](r) for the Poisson process
`trans` | vector of values of g[i,j](r) estimated by translation correction
`iso` | vector of values of g[i,j](r) estimated by Ripley isotropic correction

as required.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

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

### See Also

`pcf.ppp`, `pcfinhom`, `pcfcross`, `pcfdot.inhom`

### Examples

      data(amacrine)
      plot(pcfcross.inhom(amacrine, "on", "off", stoyan=0.1),
           legendpos="bottom")

[Package spatstat.core version 2.0-0 Index]