Jdot(X, i=1)
Jdot(X, i=1, eps, r)
Jdot(X, i=1, eps, breaks)X from which distances are measured.r.
Not normally invoked by the user. See the Details section."fv" (see fv.object).Essentially a data frame containing six numeric columns
Gdot and Fest."G" and "F"
which are respectively the outputs of Gdot
and Fest for the point pattern.i is interpreted as
a level of the factor X$marks. Beware of the usual
trap with factors: numerical values are not
interpreted in the same way as character values. See the first example.Jdot and its companions
Jcross and Jmulti
are generalisations of the function Jest
to multitype point patterns. A multitype point pattern is a spatial pattern of
points classified into a finite number of possible
``colours'' or ``types''. In the X must be a point pattern (object of class
"ppp") or any data that are acceptable to as.ppp.
It must be a marked point pattern, and the mark vector
X$marks must be a factor.
The argument i will be interpreted as a
level of the factor X$marks. (Warning: this means that
an integer value i=3 will be interpreted as the 3rd smallest level,
not the number 3).
The ``type $i$ to any type'' multitype $J$ function
of a stationary multitype point process $X$
was introduced by Van lieshout and Baddeley (1999). It is defined by
$$J_{i\bullet}(r) = \frac{1 - G_{i\bullet}(r)}{1 -
F_{\bullet}(r)}$$
where $G_{i\bullet}(r)$ is the distribution function of
the distance from a type $i$ point to the nearest other point
of the pattern, and $F_{\bullet}(r)$ is the distribution
function of the distance from a fixed point in space to the nearest
point of the pattern.
An estimate of $J_{i\bullet}(r)$
is a useful summary statistic in exploratory data analysis
of a multitype point pattern. If the pattern is
a marked Poisson point process, then
$J_{i\bullet}(r) \equiv 1$.
If the subprocess of type $i$ points is independent
of the subprocess of points of all types not equal to $i$,
then $J_{i\bullet}(r)$ equals
$J_{ii}(r)$, the ordinary $J$ function
(see Jest and Van Lieshout and Baddeley (1996))
of the points of type $i$.
Hence deviations from zero of the empirical estimate of
$J_{i\bullet} - J_{ii}$
may suggest dependence between types.
This algorithm estimates $J_{i\bullet}(r)$
from the point pattern X. It assumes that X can be treated
as a realisation of a stationary (spatially homogeneous)
random spatial point process in the plane, observed through
a bounded window.
The window (which is specified in X as X$window)
may have arbitrary shape.
Biases due to edge effects are
treated in the same manner as in Jest,
using the Kaplan-Meier and border corrections.
The main work is done by Gmulti and Fest.
The argument r is the vector of values for the
distance $r$ at which $J_{i\bullet}(r)$ should be evaluated.
The values of $r$ must be increasing nonnegative numbers
and the maximum $r$ value must exceed the radius of the
largest disc contained in the window.
Van Lieshout, M.N.M. and Baddeley, A.J. (1999) Indices of dependence between types in multivariate point patterns. Scandinavian Journal of Statistics 26, 511--532.
Jcross,
Jest,
Jmulti# Lansing woods data: 6 types of trees
data(lansing)
<testonly>lansing <- lansing[seq(1,lansing$n, by=30), ]</testonly>
Jh. <- Jdot(lansing, "hickory")
plot(Jh.)
# diagnostic plot for independence between hickories and other trees
Jhh <- Jest(lansing[lansing$marks == "hickory", ])
plot(Jhh, add=TRUE)
# synthetic example with two marks "a" and "b"
pp <- runifpoispp(50)
pp <- pp %mark% sample(c("a","b"), pp$n, replace=TRUE)
J <- Jdot(pp, "a")Run the code above in your browser using DataLab