R: Clark and Evans Aggregation Index

clarkevans {spatstat.core} | R Documentation

## Clark and Evans Aggregation Index

### Description

Computes the Clark and Evans aggregation index R for a spatial point pattern.

### Usage

    clarkevans(X, correction=c("none", "Donnelly", "cdf"),
                  clipregion=NULL)

### Arguments

`X` | A spatial point pattern (object of class `"ppp"`).
`correction` | Character vector. The type of edge correction(s) to be applied.
`clipregion` | Clipping region for the guard area correction. A window (object of class `"owin"`). See Details.

### Details

The Clark and Evans (1954) aggregation index R is a crude measure of clustering or ordering of a point pattern. It is the ratio of the observed mean nearest neighbour distance in the pattern to that expected for a Poisson point process of the same intensity. A value R>1 suggests ordering, while R<1 suggests clustering.

Without correction for edge effects, the value of `R` will be positively biased. Edge effects arise because, for a point of `X` close to the edge of the window, the true nearest neighbour may actually lie outside the window. Hence observed nearest neighbour distances tend to be larger than the true nearest neighbour distances.

The argument `correction` specifies an edge correction or several edge corrections to be applied. It is a character vector containing one or more of the options `"none"`, `"Donnelly"`, `"guard"` and `"cdf"` (which are recognised by partial matching). These edge corrections are:

"none":

  No edge correction is applied.

"Donnelly":

  Edge correction of Donnelly (1978), available for rectangular windows only. The theoretical expected value of mean nearest neighbour distance under a Poisson process is adjusted for edge effects by the edge correction of Donnelly (1978). The value of R is the ratio of the observed mean nearest neighbour distance to this adjusted theoretical mean.

"guard":

  Guard region or buffer area method. The observed mean nearest neighbour distance for the point pattern `X` is re-defined by averaging only over those points of `X` that fall inside the sub-window `clipregion`.

"cdf":

  Cumulative Distribution Function method. The nearest neighbour distance distribution function G(r) of the stationary point process is estimated by `Gest` using the Kaplan-Meier type edge correction. Then the mean of the distribution is calculated from the cdf.

Alternatively `correction="all"` selects all options.

If the argument `clipregion` is given, then the selected edge corrections will be assumed to include `correction="guard"`.

To perform a test based on the Clark-Evans index, see `clarkevans.test`.

### Value

A numeric value, or a numeric vector with named components

`naive` | R without edge correction
`Donnelly` | R using Donnelly edge correction
`guard` | R using guard region
`cdf` | R using cdf method

(as selected by `correction`). The value of the `Donnelly` component will be `NA` if the window of `X` is not a rectangle.

### Author(s)

John Rudge rudge@esc.cam.ac.uk with modifications by Adrian Baddeley Adrian.Baddeley@curtin.edu.au

### References

Clark, P.J. and Evans, F.C. (1954) Distance to nearest neighbour as a measure of spatial relationships in populations Ecology 35, 445–453.

Donnelly, K. (1978) Simulations to determine the variance and edge-effect of total nearest neighbour distance. In I. Hodder (ed.) Simulation studies in archaeology, Cambridge/New York: Cambridge University Press, pp 91–95.

### See Also

`clarkevans.test`, `hopskel`, `nndist`, `Gest`

### Examples

      # Example of a clustered pattern
      clarkevans(redwood)

      # Example of an ordered pattern
      clarkevans(cells)

      # Random pattern
      X <- rpoispp(100)
      clarkevans(X)

      # How to specify a clipping region
      clip1 <- owin(c(0.1,0.9),c(0.1,0.9))
      clip2 <- erosion(Window(cells), 0.1)
      clarkevans(cells, clipregion=clip1)
      clarkevans(cells, clipregion=clip2)

[Package spatstat.core version 2.0-0 Index]