# nncorr

##### Nearest-Neighbour Correlation Indices of Marked Point Pattern

Computes nearest-neighbour correlation indices of a marked point
pattern, including the nearest-neighbour mark product index
(default case of `nncorr`

),
the nearest-neighbour mark index (`nnmean`

),
and the nearest-neighbour variogram index (`nnvario`

).

- Keywords
- spatial, nonparametric

##### Usage

```
nncorr(X,
f = function(m1, m2) { m1 * m2 },
...,
use = "all.obs", method = c("pearson", "kendall", "spearman"),
denominator=NULL)
nnmean(X)
nnvario(X)
```

##### Arguments

- X
- The observed point pattern.
An object of class
`"ppp"`

. - f
- Function $f$ used in the definition of the
nearest neighbour correlation. There is a sensible default
that depends on the type of marks of
`X`

. - ...
- Extra arguments passed to
`f`

. - use,method
- Arguments passed to the standard correlation function
`cor`

. - denominator
- Internal use only.

##### Details

The nearest neighbour correlation index $\bar n_f$ of a marked point process $X$ is a number measuring the dependence between the mark of a typical point and the mark of its nearest neighbour.

The command `nncorr`

computes the nearest neighbour correlation index
based on any test function `f`

provided by the user.
The default behaviour of `nncorr`

is to compute the
nearest neighbour mark product index.
The commands `nnmean`

and `nnvario`

are
convenient abbreviations for other special choices of `f`

.

In the default case, `nncorr(X)`

computes three different
versions of the nearest-neighbour correlation index:
the unnormalised, normalised, and classical correlations.
[object Object],[object Object],[object Object]

In the default case where `f`

is not given,
`nncorr(X)`

computes

- If the marks of
`X`

are real numbers, the unnormalised and normalised versions of the nearest-neighbour product index$E[M \, M^\ast]$, and the classical correlation between$M$and$M^\ast$. - If the marks of
`X`

are factor valued, the unnormalised and normalised versions of the nearest-neighbour equality index$P[M = M^\ast]$.

The wrapper functions `nnmean`

and `nnvario`

compute the correlation indices for two special choices of the
function $f(m_1,m_2)$.

`nnmean`

computes the correlation indices for$f(m_1,m_2) = m_1$. The unnormalised index is simply the mean value of the mark of the neighbour of a typical point,$E[M^\ast]$, while the normalised index is$E[M^\ast]/E[M]$, the ratio of the mean mark of the neighbour of a typical point to the mean mark of a typical point.`nnvario`

computes the correlation indices for$f(m_1,m_2) = (1/2) (m_1-m_2)^2$.

The argument `X`

must be a point pattern (object of class
`"ppp"`

) and must be a marked point pattern.
(The marks may be a data frame, containing several columns of mark variables;
each column is treated separately.)

If the argument `f`

is given, it
must be a function, accepting two arguments `m1`

and `m2`

which are vectors of equal length containing mark
values (of the same type as the marks of `X`

).
It must return a vector of numeric
values of the same length as `m1`

and `m2`

.
The values must be non-negative.

The arguments `use`

and `method`

control
the calculation of the classical correlation using `cor`

,
as explained in the help file for `cor`

.

Other arguments may be passed to `f`

through the `...`

argument.
This algorithm assumes that `X`

can be treated
as a realisation of a stationary (spatially homogeneous)
random spatial point process in the plane, observed through
a bounded window.
The window (which is specified in `X`

as `X$window`

)
may have arbitrary shape.
Biases due to edge effects are
treated using the

##### Value

- Labelled vector of length 2 or 3 containing the unnormalised and normalised nearest neighbour correlations, and the classical correlation if appropriate. Alternatively a matrix with 2 or 3 rows, containing this information for each mark variable.

##### References

Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.

##### Examples

```
data(finpines)
nncorr(finpines)
# heights of neighbouring trees are slightly negatively correlated
data(amacrine)
nncorr(amacrine)
# neighbouring cells are usually of different type
```

*Documentation reproduced from package spatstat, version 1.41-1, License: GPL (>= 2)*