# markcorrint

##### Mark Correlation Integral

Estimates the mark correlation integral of a marked point pattern.

- Keywords
- spatial, nonparametric

##### Usage

```
markcorrint(X, f = NULL, r = NULL,
correction = c("isotropic", "Ripley", "translate"), ...,
f1 = NULL, normalise = TRUE, returnL = FALSE, fargs = NULL)
```

##### Arguments

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

or something acceptable to`as.ppp`

. - f
- Optional. Test function $f$ used in the definition of the mark correlation function. An Rfunction with at least two arguments. There is a sensible default.
- r
- Optional. Numeric vector. The values of the argument $r$ at which the mark correlation function $k_f(r)$ should be evaluated. There is a sensible default.
- correction
- A character vector containing any selection of the
options
`"isotropic"`

,`"Ripley"`

or`"translate"`

. It specifies the edge correction(s) to be applied. - ...
- Ignored.
- f1
- An alternative to
`f`

. If this argument is given, then $f$ is assumed to take the form $f(u,v)=f_1(u)f_1(v)$. - normalise
- If
`normalise=FALSE`

, compute only the numerator of the expression for the mark correlation. - returnL
- Compute the analogue of the K-function if
`returnL=FALSE`

or the analogue of the L-function if`returnL=TRUE`

. - fargs
- Optional. A list of extra arguments to be passed to the function
`f`

or`f1`

.

##### Details

Given a marked point pattern `X`

,
this command estimates the weighted indefinite integral
$$K_f(r) = 2 \pi \int_0^r s k_f(s) ds$$
of the mark correlation function $k_f(r)$.
See `markcorr`

for a definition of the
mark correlation function.

The use of the weighted indefinite integral was advocated by Penttinen et al (1992). The relationship between $K_f$ and $k_f$ is analogous to the relationship between the classical K-function $K(r)$ and the pair correlation function $g(r)$.

If `returnL=FALSE`

then the function $K_f(r)$ is returned;
otherwise the function
$$L_f(r) = \sqrt{K_f(r)/pi}$$
is returned.

##### Value

- An object of class
`"fv"`

(see`fv.object`

). Essentially a data frame containing numeric columns r the values of the argument $r$ at which the mark correlation integral $K_f(r)$ has been estimated theo the theoretical value of $K_f(r)$ when the marks attached to different points are independent, namely $\pi r^2$ - together with a column or columns named
`"iso"`

and/or`"trans"`

, according to the selected edge corrections. These columns contain estimates of the mark correlation integral $K_f(r)$ obtained by the edge corrections named (if`returnL=FALSE`

).

##### References

Penttinen, A., Stoyan, D. and Henttonen, H. M. (1992)
Marked point processes in forest statistics.
*Forest Science* **38** (1992) 806-824.

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008)
*Statistical analysis and modelling of spatial point patterns*.
Chichester: John Wiley.

##### See Also

`markcorr`

to estimate the mark correlation function.

##### Examples

```
# CONTINUOUS-VALUED MARKS:
# (1) Spruces
# marks represent tree diameter
data(spruces)
# mark correlation function
ms <- markcorrint(spruces)
plot(ms)
# (2) simulated data with independent marks
X <- rpoispp(100)
X <- X %mark% runif(X$n)
Xc <- markcorrint(X)
plot(Xc)
# MULTITYPE DATA:
# Hughes' amacrine data
# Cells marked as 'on'/'off'
data(amacrine)
M <- markcorrint(amacrine, function(m1,m2) {m1==m2},
correction="translate")
plot(M)
```

*Documentation reproduced from package spatstat, version 1.28-1, License: GPL (>= 2)*