pcfcross.inhom: Inhomogeneous Multitype Pair Correlation Function...

In spatstat.explore: Exploratory Data Analysis for the 'spatstat' Family

Inhomogeneous Multitype Pair Correlation Function (Cross-Type)

Description

Estimates the inhomogeneous cross-type pair correlation function for a multitype point pattern.

Usage

pcfcross.inhom(X, i, j, lambdaI = NULL, lambdaJ = NULL, ...,
               r = NULL, breaks = NULL,
               kernel="epanechnikov", bw=NULL, adjust.bw = 1, stoyan=0.15,
               correction = c("isotropic", "Ripley", "translate"),
               sigma = NULL, adjust.sigma = 1, varcov = NULL)

Arguments

X	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).
i	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).
j	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).
lambdaI	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.
lambdaJ	Optional. Values of the estimated intensity function of the points of type j. A numeric vector, pixel image or function(x,y).
r	Vector of values for the argument r at which g_{ij}(r) should be evaluated. There is a sensible default.
breaks	This argument is for internal use only.
kernel	Choice of one-dimensional smoothing kernel, passed to density.default.
bw	Bandwidth for one-dimensional smoothing kernel, passed to density.default.
adjust.bw	Numeric value. bw will be multiplied by this value.
...	Other arguments passed to the one-dimensional kernel density estimation function density.default.
stoyan	Bandwidth coefficient; see Details.
correction	Choice of edge correction.
sigma, varcov	Optional arguments passed to density.ppp to control the smoothing bandwidth, when lambdaI or lambdaJ is estimated by spatial kernel smoothing.
adjust.sigma	Numeric value. sigma will be multiplied by this value.

Details

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.

Value

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_{ij}(r) has been estimated
theo	vector of values equal to 1, the theoretical value of g_{ij}(r) for the Poisson process
trans	vector of values of g_{ij}(r) estimated by translation correction
iso	vector of values of g_{ij}(r) estimated by Ripley isotropic correction

as required.

Author(s)

\adrian

and \rolf

See Also

pcf.ppp, pcfinhom, pcfcross, pcfdot.inhom

Examples

  plot(pcfcross.inhom(amacrine, "on", "off", stoyan=0.1),
       legendpos="bottom")

spatstat.explore documentation built on Oct. 22, 2024, 9:07 a.m.