Jmulti {spatstat} | R Documentation |
For a marked point pattern, estimate the multitype J function summarising dependence between the points in subset I and those in subset J.
Jmulti(X, I, J, eps=NULL, r=NULL, breaks=NULL, ..., disjoint=NULL, correction=NULL)
X |
The observed point pattern, from which an estimate of the multitype distance distribution function J[IJ](r) will be computed. It must be a marked point pattern. See under Details. |
I |
Subset of points of |
J |
Subset of points in |
eps |
A positive number.
The pixel resolution of the discrete approximation to Euclidean
distance (see |
r |
numeric vector. The values of the argument r at which the distribution function J[IJ](r) should be evaluated. There is a sensible default. First-time users are strongly advised not to specify this argument. See below for important conditions on r. |
breaks |
An alternative to the argument |
... |
Ignored. |
disjoint |
Optional flag indicating whether
the subsets |
correction |
Optional. Character string specifying the edge correction(s)
to be used. Options are |
The function Jmulti
generalises Jest
(for unmarked point
patterns) and Jdot
and Jcross
(for
multitype point patterns) to arbitrary marked point patterns.
Suppose X[I], X[J] are subsets, possibly overlapping, of a marked point process. Define
J[IJ](r) = (1 - G[IJ](r))/(1 - F[J](r))
where F[J](r) is the cumulative distribution function of the distance from a fixed location to the nearest point of X[J], and GJ(r) is the distribution function of the distance from a typical point of X[I] to the nearest distinct point of X[J].
The argument X
must be a point pattern (object of class
"ppp"
) or any data that are acceptable to as.ppp
.
The arguments I
and J
specify two subsets of the
point pattern X
. They may be logical vectors of length equal to
npoints(X)
, or integer vectors with entries in the range 1 to
npoints(X)
, etc.
It is assumed 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
.
The argument r
is the vector of values for the
distance r at which J[IJ](r) should be evaluated.
It is also used to determine the breakpoints
(in the sense of hist
)
for the computation of histograms of distances. The reduced-sample and
Kaplan-Meier estimators are computed from histogram counts.
In the case of the Kaplan-Meier estimator this introduces a discretisation
error which is controlled by the fineness of the breakpoints.
First-time users would be strongly advised not to specify r
.
However, if it is specified, r
must satisfy r[1] = 0
,
and max(r)
must be larger than the radius of the largest disc
contained in the window. Furthermore, the successive entries of r
must be finely spaced.
An object of class "fv"
(see fv.object
).
Essentially a data frame containing six numeric columns
r |
the values of the argument r at which the function J[IJ](r) has been estimated |
rs |
the “reduced sample” or “border correction” estimator of J[IJ](r) |
km |
the spatial Kaplan-Meier estimator of J[IJ](r) |
han |
the Hanisch-style estimator of J[IJ](r) |
un |
the uncorrected estimate of J[IJ](r),
formed by taking the ratio of uncorrected empirical estimators
of 1 - G[IJ](r)
and 1 - F[J](r), see
|
theo |
the theoretical value of J[IJ](r) for a marked Poisson process with the same estimated intensity, namely 1. |
Adrian Baddeley Adrian.Baddeley@csiro.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner r.turner@auckland.ac.nz
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.
data(longleaf) # Longleaf Pine data: marks represent diameter Jm <- Jmulti(longleaf, marks(longleaf) <= 15, marks(longleaf) >= 25) plot(Jm)