markcrosscorr(X, r = NULL,
correction = c("isotropic", "Ripley", "translate"),
method = "density", ..., normalise = TRUE, Xname = NULL)"ppp" or something acceptable to
as.ppp."isotropic", "Ripley", "translate",
"translation", "none" or "best".
It specifies the edge correction(s) t"density",
"loess",
"sm" and "smrep".normalise=FALSE,
compute only the numerator of the expression for the
mark correlation.X."fasp") containing
the mark cross-correlation functions for each possible pair
of columns of marks. Next, each pair of columns is considered, and the mark
cross-correlation is defined as
$$k_{mm}(r) = \frac{E_{0u}[M_i(0) M_j(u)]}{E[M_i,M_j]}$$
where $E_{0u}$ denotes the conditional expectation
given that there are points of the process at the locations
$0$ and $u$ separated by a distance $r$.
On the numerator,
$M_i(0)$ and $M_j(u)$
are the marks attached to locations $0$ and $u$ respectively
in the $i$th and $j$th columns of marks respectively.
On the denominator, $M_i$ and $M_j$ are
independent random values drawn from the
$i$th and $j$th columns of marks, respectively,
and $E$ is the usual expectation.
Note that $k_{mm}(r)$ is not a ``correlation''
in the usual statistical sense. It can take any
nonnegative real value. The value 1 suggests ``lack of correlation'':
if the marks attached to the points of X are independent
and identically distributed, then
$k_{mm}(r) \equiv 1$.
The argument X must be a point pattern (object of class
"ppp") or any data that are acceptable to as.ppp.
It must be a marked point pattern.
The cross-correlations are estimated in the same manner as
for markcorr.
markcorr# The dataset 'betacells' has two columns of marks:
# 'type' (factor)
# 'area' (numeric)
if(interactive()) plot(betacells)
plot(markcrosscorr(betacells))Run the code above in your browser using DataLab