Inhomogeneous Multitype Pair Correlation Function (Cross-Type)
Estimates the inhomogeneous cross-type pair correlation function for a multitype point pattern.
pcfcross.inhom(X, i, j, lambdaI = NULL, lambdaJ = NULL, ...,
r = NULL, breaks = NULL,
kernel="epanechnikov", bw=NULL, stoyan=0.15,
correction = c("isotropic", "Ripley", "translate"),
sigma = NULL, varcov = NULL)X |
The observed point pattern, from which an estimate of the inhomogeneous 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 |
The type (mark value)
of the points in |
j |
The type (mark value)
of the points in |
lambdaI |
Optional.
Values of the estimated intensity function of the points of type |
lambdaJ |
Optional.
Values of the estimated intensity function of the points of type |
r |
Vector of values for the argument r at which g[i,j](r) should be evaluated. There is a sensible default. |
breaks |
This argument is for internal use only. |
kernel |
Choice of smoothing kernel, passed to |
bw |
Bandwidth for smoothing kernel, passed to |
... |
Other arguments passed to the kernel density estimation
function |
stoyan |
Bandwidth coefficient; see Details. |
correction |
Choice of edge correction. |
sigma,varcov |
Optional arguments passed to |
The inhomogeneous cross-type pair correlation function g[i,j](r) is a summary of the dependence between two types of points in a multitype spatial point process that does not have a uniform density of points.
The best intuitive interpretation is the following: the probability p(r) of finding two points, of types i and j respectively, at locations x and y separated by a distance r is equal to
p(r) = lambda[i](x) * lambda[j](y) * g(r) dx dy
where lambda[i] is the intensity function of the process of points of type i. For a multitype Poisson point process, this probability is p(r) = lambda[i](x) * lambda[j](y) so g[i,j](r) = 1.
The command pcfcross.inhom estimates the inhomogeneous
pair correlation using a modified version of
the algorithm in pcf.ppp.
If the arguments lambdaI and lambdaJ are missing or
null, they are estimated from X by kernel smoothing using a
leave-one-out estimator.
A function value table (object of class "fv").
Essentially a data frame containing the variables
r |
the vector of values of the argument r at which the inhomogeneous cross-type pair correlation function g[i,j](r) has been estimated |
theo |
vector of values equal to 1, the theoretical value of g[i,j](r) for the Poisson process |
trans |
vector of values of g[i,j](r) estimated by translation correction |
iso |
vector of values of g[i,j](r) estimated by Ripley isotropic correction |
as required.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
data(amacrine)
plot(pcfcross.inhom(amacrine, "on", "off", stoyan=0.1),
legendpos="bottom")Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.