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

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

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.

- 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.

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

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`

.

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.

`clarkevans.test`

,
`hopskel`

,
`nndist`

,
`Gest`

```
# 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)
```

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