pcfcross {spatstat} | R Documentation |
Calculates an estimate of the cross-type pair correlation function for a multitype point pattern.
pcfcross(X, i, j, ...)
X |
The observed point pattern, from which an estimate of the cross-type pair correlation function g[i,j](r) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). |
i |
Number or character string identifying the type (mark value)
of the points in |
j |
Number or character string identifying the type (mark value)
of the points in |
... |
Arguments passed to |
The cross-type pair correlation function
is a generalisation of the pair correlation function pcf
to multitype point patterns.
For two locations x and y separated by a distance r, the probability p(r) of finding a point of type i at location x and a point of type j at location y is
p(r) = lambda[i] * lambda[j] * g[i,j](r) dx dy
where lambda[i] is the intensity of the points
of type i.
For a completely random Poisson marked point process,
p(r) = lambda[i] * lambda[j]
so g[i,j](r) = 1.
Indeed for any marked point pattern in which the points of type i
are independent of the points of type j
,
the theoretical value of the cross-type pair correlation is
g[i,j](r) = 1.
For a stationary multitype point process, the cross-type pair correlation function between marks i and j is formally defined as
g(r) = K[i,j]'(r)/ ( 2 * pi * r)
where K[i,j]'(r) is the derivative of
the cross-type K function K[i,j](r).
of the point process. See Kest
for information
about K(r).
The command pcfcross
computes a kernel estimate of
the cross-type pair correlation function between marks i and
j. It uses pcf.ppp
to compute kernel estimates
of the pair correlation functions for several unmarked point patterns,
and uses the bilinear properties of second moments to obtain the
cross-type pair correlation.
See pcf.ppp
for a list of arguments that control
the kernel estimation.
The companion function pcfdot
computes the
corresponding analogue of Kdot
.
An object of class "fv"
, see fv.object
,
which can be plotted directly using plot.fv
.
Essentially a data frame containing columns
r |
the vector of values of the argument r at which the function g[i,j] has been estimated |
theo |
the theoretical value g[i,j](r) = r for independent marks. |
together with columns named
"border"
, "bord.modif"
,
"iso"
and/or "trans"
,
according to the selected edge corrections. These columns contain
estimates of the function g[i,j]
obtained by the edge corrections named.
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
Mark connection function markconnect
.
Multitype pair correlation pcfdot
.
data(amacrine) p <- pcfcross(amacrine, "off", "on") p <- pcfcross(amacrine, "off", "on", stoyan=0.1) plot(p)