spatstat.core: pcfdot.inhom – R documentation

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pcfdot.inhom

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, stoyan=0.15,
               correction = c("isotropic", "Ripley", "translate"),
               sigma = NULL, varcov = NULL)

Arguments

`X`	The observed point pattern, from which an estimate of the inhomogeneous multitype pair correlation function g[i.](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.](r) should be evaluated. There is a sensible default.
`breaks`	This argument is for internal use only.
`kernel`	Choice of smoothing kernel, passed to `density.default`.
`bw`	Bandwidth for smoothing kernel, passed to `density.default`.
`...`	Other arguments passed to the 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 `lambdadot` is estimated by kernel smoothing.

Details

The inhomogeneous multitype (type i to any type) pair correlation function g[i.](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) dx dy

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.](r) = 1.

The command pcfdot.inhom estimates the inhomogeneous multitype pair correlation using a modified version of the algorithm in pcf.ppp.

If the arguments lambdaI and lambdadot are missing or null, they are estimated from X by kernel smoothing using a leave-one-out estimator.

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.](r) has been estimated
`theo`	vector of values equal to 1, the theoretical value of g[i.](r) for the Poisson process
`trans`	vector of values of g[i.](r) estimated by translation correction
`iso`	vector of values of g[i.](r) estimated by Ripley isotropic correction

as required.

Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

Examples

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

spatstat.core

Core Functionality of the 'spatstat' Family

v2.1-2

GPL (>= 2)

Authors

Adrian Baddeley [aut, cre], Rolf Turner [aut], Ege Rubak [aut], Kasper Klitgaard Berthelsen [ctb], Achmad Choiruddin [ctb], Jean-Francois Coeurjolly [ctb], Ottmar Cronie [ctb], Tilman Davies [ctb], Julian Gilbey [ctb], Yongtao Guan [ctb], Ute Hahn [ctb], Kassel Hingee [ctb], Abdollah Jalilian [ctb], Marie-Colette van Lieshout [ctb], Greg McSwiggan [ctb], Tuomas Rajala [ctb], Suman Rakshit [ctb], Dominic Schuhmacher [ctb], Rasmus Plenge Waagepetersen [ctb], Hangsheng Wang [ctb]

Initial release

2021-04-17