pcfmulti.inhom: Inhomogeneous Multitype Pair Correlation Function

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

Inhomogeneous Multitype Pair Correlation Function

Description

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

Usage

pcfmulti.inhom(X, I, J, lambdaI = NULL, lambdaJ = NULL, ...,
               lambdaX=NULL,
               r = NULL, breaks = NULL, rmax = NULL,
               adaptive = FALSE,
               kernel = "epanechnikov", bw = NULL, h = NULL, bw.args = list(),
               stoyan = 0.15, adjust.bw = 1,
               correction = c("translate", "Ripley"),
               divisor = c("a", "r", "d", "t"),
               zerocor = c("convolution", "reflection",
                         "bdrykern", "JonesFoster", "weighted",
                         "none", "good", "best"),
               nsmall = 300,
               gref = NULL, tau = 0,
               sigma = NULL, adjust.sigma = 1, varcov = NULL,
               update = TRUE, leaveoneout = TRUE,
               Iname = "points satisfying condition I",
               Jname = "points satisfying condition J",
               IJexclusive = FALSE, Ilevels=NULL, Jlevels=NULL,
               close = 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	Subset index specifying the points of X from which distances are measured.
J	Subset index specifying the points in X to which distances are measured.
lambdaI	Optional. Values of the estimated intensity function of the points belonging to subset I. (Ignored if lambdaX is given.) Either a numeric vector giving the intensity values at the data points of subset I, a pixel image (object of class "im") giving the intensity values of points of subset I at all locations, a function(x,y) which can be evaluated to give the intensity value of points of subset I at any location, or a fitted point process model (class "ppm", "kppm", "dppm" or "slrm") which could be used to predict the intensity values of points of subset J at all locations. If lambdaI is an unmarked point process model, it is assumed to have been fitted to X[I]; if it is a multitype point process model, it is assumed to have been fitted to X, and the argument Ilevels is required.
lambdaJ	Optional. Values of the estimated intensity function of the points belonging to subset J. A numeric vector, pixel image, function(x,y), or fitted point process model. Ignored if lambdaX is given.
...	Ignored.
lambdaX	Optional. Alternative to lambdaI and lambdaJ. Data which can be used to calculate the intensity functions of both the subsets I and J. A list of pixel images (one image for each possible type of point), a function(x,y,mark) giving the intensity at each location for each possible type of point, a numeric matrix with one row for each point in X and one column for each possible type of point, or a fitted multitype point process model (class "ppm"). The arguments Ilevels and Jlevels are required in this case.
r	Vector of values for the argument r at which g(r) should be evaluated. There is a sensible default.
breaks	Internal use only.
rmax	Optional. Maximum desired value of the argument r. A single numeric value. There is a sensible default.
adaptive	Logical value specifying whether to use adaptive kernel smoothing (adaptive=TRUE) or fixed-bandwidth kernel smoothing (adaptive=FALSE, the default).
kernel	Choice of smoothing kernel, passed to density.default.
bw	Bandwidth for smoothing kernel. Either a single numeric value giving the standard deviation of the kernel, or a character string specifying a bandwidth selection rule, or a function that computes the selected bandwidth. See Details.
h	Kernel halfwidth h (incompatible with argument bw). A numerical value. The parameter h is defined as the half-width of the support of the kernel, except for the Gaussian kernel where h is the standard deviation.
bw.args	Optional. List of additional arguments to be passed to bw when bw is a function. Alternatively, bw may be a function that should be applied to X to produce a list of additional arguments.
stoyan	Coefficient for default bandwidth rule.
adjust.bw	Numerical adjustment factor for the bandwidth. The bandwidth actually used is bw * adjust.bw. This makes it easy to specify choices like ‘half the selected bandwidth’.
correction	String (partially matched) specifying the choice or choices of spatial edge correction. Options include "translate" for the translation correction, "isotropic" or "Ripley" for Ripley's isotropic correction, and "none" for no edge correction.
divisor	String specifying the choice of estimator. See pcf.ppp.
zerocor	String (partially matched) specifying a correction for the boundary effect bias at r=0. Possible values are "none", "weighted", "convolution", "reflection", "bdrykern" and "JonesFoster". See pcf.ppp.
nsmall	Optional. Integer. The maximum number of data points for which the default value of zerocor will be "JonesFoster".
gref	Optional. A pair correlation function that will be used as the reference for the transformation to uniformity, when divisor="t". Either a function in the R language giving the pair correlation function, or a fitted model (object of class "kppm", "dppm", "ppm" or "slrm") or a theoretical point process model (object of class "zclustermodel" or "detpointprocfamily") for which the pair correlation function can be computed.
tau	Optional shrinkage coefficient. A single numeric value.
sigma, varcov	Optional arguments passed to density.ppp to control the smoothing bandwidth, when lambda is estimated by kernel smoothing.
adjust.sigma	Numeric value. sigma will be multiplied by this value.
update	Logical value indicating what to do when lambdaI, lambdaJ or lambdaX is a fitted point process model (class "ppm", "kppm" or "dppm"). If update=TRUE (the default), the model will first be updated (refitted to the data) before the fitted intensity lambdaI or lambdaJ at the data points is computed. If update=FALSE, the fitted intensity of the model will be computed without re-fitting the model.
leaveoneout	Logical value (passed to density.ppp or fitted.ppm) specifying whether to use a leave-one-out rule when calculating the intensity.
Iname, Jname	Optional. Character strings describing the members of the subsets I and J.
IJexclusive	Logical value indicating whether the subsets I and J are guaranteed to be mutually exclusive.
Ilevels	Character vector containing the types of points (levels of marks(X)) which comprise the subset I. Required when lambdaX is given or when lambdaI is a multitype point process model.
Jlevels	Character vector containing the types of points (levels of marks(X)) which comprise the subset J. Required when lambdaX is given or when lambdaJ is a multitype point process model.
close	Advanced use only. Precomputed data obtained from crosspairs.

Details

This is a generalisation of pcfcross.inhom to arbitrary collections of points.

The algorithm measures the distance from each data point in subset I to each data point in subset J, excluding identical pairs of points. The distances are weighted by the reciprocal intensity (as described below), then kernel-smoothed and renormalised to form a pair correlation function.

The contribution from each pair of data points u,v is weighted by 1/(\lambda_I(u) \lambda_J(v)) where \lambda_I(u) is the estimated intensity of points belonging to subset I at location u, and similarly \lambda_J(u) is the estimated intensity of points belonging to subset J at location v.

The estimated intensities \lambda_I(u) and \lambda_J(u) are determined as follows.

• If lambdaX is given, then it should provide data giving the intensities of both subsets I and J. It may be

  • A list of pixel images, one for each possible type of point

  • A function(x,y,mark) which can be evaluated to give the intensity of each type of point at any location

  • A matrix with one row for each data point in X and one column for each possible type of point, giving the estimated intensity of each type of point at each data location

  • A fitted point process model (class "lppm" or "ppm") that was fitted to a multitype point pattern. If update=TRUE, this model will be re-fitted to the data pattern X. Then the fitted intensities for subsets I and J will be computed (using the information Ilevels and Jlevels).

• Otherwise if lambdaI is given, it may be

  • A pixel image

  • A function(x,y)

  • A numeric vector with one entry for each data point in X[I]

  • A fitted point process model (class "lppm" or "ppm") that was fitted to a multitype point pattern. If update=TRUE, this model will be re-fitted to the data pattern X. Then the intensity of this model for the subset I will be computed (using the information Ilevels).

  • A fitted point process model (class "lppm", "ppm", "kppm", "dppm" or "slrm") that was fitted to an unmarked point pattern. If update=TRUE, this model will be re-fitted to the relevant subset of the data, unmark(X[I]). Then the intensity of this fitted model will be computed.

• Otherwise if lambda is missing or NULL, then a kernel estimate of the intensity \lambda_I(u) will be computed by applying density.ppp to X[I] using the arguments sigma, adjust.sigma, varcov and leaveoneout.

• Similarly for lambdaJ.

The smoothing algorithm is a multitype version of the smoothing algorithm in pcf.ppp. See pcf.ppp for detailed documentation of the arguments correction, divisor, zerocor, and other smoothing arguments.

Value

An object of class "fv".

Author(s)

\spatstatAuthorsComma

, \tilman and \martinH.

See Also

pcfcross.inhom, pcf.ppp.

Examples

  adult <- (marks(longleaf) >= 30)
  juvenile <- !adult
  p <- pcfmulti.inhom(longleaf, adult, juvenile)

spatstat.explore documentation built on March 22, 2026, 5:06 p.m.