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 toas.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 ifreturnL=TRUE
. - fargs
- Optional. A list of extra arguments to be passed to the function
f
orf1
.
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"
(seefv.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 (ifreturnL=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)