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, rmax=NULL,
kernel="epanechnikov", bw=NULL, adjust.bw = 1, stoyan=0.15,
correction = c("isotropic", "Ripley", "translate"),
sigma = NULL, adjust.sigma = 1, varcov = NULL)A function value table (object of class "fv").
Essentially a data frame containing the variables
the vector of values of the argument \(r\) at which the inhomogeneous cross-type pair correlation function \(g_{ij}(r)\) has been estimated
vector of values equal to 1, the theoretical value of \(g_{ij}(r)\) for the Poisson process
vector of values of \(g_{ij}(r)\) estimated by translation correction
vector of values of \(g_{ij}(r)\) estimated by Ripley isotropic correction
as required.
The inhomogeneous cross-type pair correlation function \(g_{ij}(r)\) 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 $$ p(r) = \lambda_i(x) lambda_j(y) g(r) \,{\rm d}x \, {\rm d}y $$ 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 \(g_{ij}(r) = 1\).
The command pcfcross.inhom estimates the inhomogeneous
pair correlation using a modified version of
the algorithm in pcf.ppp.
The arguments bw and adjust.bw control the
degree of one-dimensional smoothing of the estimate of pair correlation.
If the arguments lambdaI and/or lambdaJ are missing or
null, they will be estimated from X by spatial kernel smoothing
using a leave-one-out estimator, computed by density.ppp.
The arguments sigma, varcov
and adjust.sigma control the degree of spatial smoothing.
pcf.ppp,
pcfinhom,
pcfcross,
pcfdot.inhom
plot(pcfcross.inhom(amacrine, "on", "off", stoyan=0.1),
legendpos="bottom")
Run the code above in your browser using DataLab