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

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

Inhomogeneous Multitype Pair Correlation Function (Type-i-To-Any-Type)

Description

Estimates the inhomogeneous multitype pair correlation function (from type i to any type) for a multitype point pattern.

Usage

pcfdot.inhom(X, i, lambdaI = NULL, lambdadot = 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 multitype pair correlation function g_{i\bullet}(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).
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.
lambdadot	Optional. Values of the estimated intensity function of the point pattern X. A numeric vector, pixel image or function(x,y).
r	Vector of values for the argument r at which g_{i\bullet}(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 and/or lambdadot is estimated by spatial kernel smoothing.
adjust.sigma	Numeric value. sigma will be multiplied by this value.

Details

The inhomogeneous multitype (type i to any type) pair correlation function g_{i\bullet}(r) is a summary of the dependence between different 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 a point of type i at location x and another point of any type at location y, where x and y are separated by a distance r, is equal to

p(r) = \lambda_i(x) lambda(y) g(r) \,{\rm d}x \, {\rm d}y

where \lambda_i is the intensity function of the process of points of type i, and where \lambda is the intensity function of the points of all types. For a multitype Poisson point process, this probability is p(r) = \lambda_i(x) \lambda(y) so g_{i\bullet}(r) = 1.

The command pcfdot.inhom estimates the inhomogeneous multitype 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 lambdadot 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 multitype pair correlation function g_{i\bullet}(r) has been estimated
theo	vector of values equal to 1, the theoretical value of g_{i\bullet}(r) for the Poisson process
trans	vector of values of g_{i\bullet}(r) estimated by translation correction
iso	vector of values of g_{i\bullet}(r) estimated by Ripley isotropic correction

as required.

Author(s)

\adrian

and \rolf

See Also

pcf.ppp, pcfinhom, pcfdot, pcfcross.inhom

Examples

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

spatstat.explore documentation built on Oct. 23, 2023, 1:07 a.m.