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)The observed point pattern, from which an estimate of the inhomogeneous cross-type pair correlation function \(g_{ij}(r)\) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor).
The type (mark value)
of the points in X from which distances are measured.
A character string (or something that will be converted to a
character string).
Defaults to the first level of marks(X).
The type (mark value)
of the points in X to which distances are measured.
A character string (or something that will be
converted to a character string).
Defaults to the second level of marks(X).
Optional.
Values of the estimated intensity function of the points of type i.
Either a vector giving the intensity values
at the points of type i,
a pixel image (object of class "im") giving the
intensity values at all locations, or a function(x,y) which
can be evaluated to give the intensity value at any location.
Optional.
Values of the estimated intensity function of the points of type j.
A numeric vector, pixel image or function(x,y).
Vector of values for the argument \(r\) at which \(g_{ij}(r)\) should be evaluated. There is a sensible default.
This argument is for internal use only.
Choice of smoothing kernel, passed to density.default.
Bandwidth for smoothing kernel, passed to density.default.
Other arguments passed to the kernel density estimation
function density.default.
Bandwidth coefficient; see Details.
Choice of edge correction.
Optional arguments passed to density.ppp
to control the smoothing bandwidth, when lambdaI or
lambdaJ is estimated by kernel smoothing.
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
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.
If the arguments lambdaI and lambdaJ are missing or
null, they are estimated from X by kernel smoothing using a
leave-one-out estimator.
# NOT RUN {
data(amacrine)
plot(pcfcross.inhom(amacrine, "on", "off", stoyan=0.1),
legendpos="bottom")
# }
Run the code above in your browser using DataLab