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) to be applied.
Alternatively correction="all" selects all options.
"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, $Mi$ and $Mj$ 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
$k[mm](r) = 1$.
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))
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