spatstat.explore (version 3.3-1)

Gdot.inhom: Inhomogeneous Multitype G Dot Function

Description

For a multitype point pattern, estimate the inhomogeneous version of the dot \(G\) function, which is the distribution of the distance from a point of type \(i\) to the nearest other point of any type, adjusted for spatially varying intensity.

Usage

Gdot.inhom(X, i,
              lambdaI = NULL, lambdadot = NULL, lambdamin = NULL,
              ...,
              r = NULL, ReferenceMeasureMarkSetI = NULL, ratio = FALSE)

Value

An object of class "fv" (see fv.object) containing estimates of the inhomogeneous dot type \(G\) function.

Arguments

X

The observed point pattern, from which an estimate of the inhomogeneous dot type \(G\) function \(G_{i\bullet}(r)\) will be computed. It must be a multitype point pattern (a marked point pattern whose marks are a factor). See under Details.

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 of the sub-process of points of type i. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the type i points in X, a fitted point process model (object of class "ppm" or "kppm" or "dppm"), or a function(x,y) which can be evaluated to give the intensity value at any location.

lambdadot

Optional. Values of the estimated intensity of the entire point process, Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the points in X, a fitted point process model (object of class "ppm" or "kppm" or "dppm"), or a function(x,y) which can be evaluated to give the intensity value at any location.

lambdamin

Optional. The minimum possible value of the intensity over the spatial domain. A positive numerical value.

...

Ignored.

r

vector of values for the argument \(r\) at which the inhomogeneous dot type \(G\) function \(G_{i\bullet}(r)\) should be evaluated. Not normally given by the user; there is a sensible default.

ReferenceMeasureMarkSetI

Optional. The total measure of the mark set. A positive number.

ratio

Logical value indicating whether to save ratio information.

Warnings

The argument i is interpreted as a level of the factor X$marks. It is converted to a character string if it is not already a character string. The value i=1 does not refer to the first level of the factor.

Author

Adrian Baddeley , Rolf Turner and Ege Rubak

Details

This is a generalisation of the function Gdot to include an adjustment for spatially inhomogeneous intensity, in a manner similar to the function Ginhom.

The argument lambdaI supplies the values of the intensity of the sub-process of points of type i. It may be either

a pixel image

(object of class "im") which gives the values of the type i intensity at all locations in the window containing X;

a numeric vector

containing the values of the type i intensity evaluated only at the data points of type i. The length of this vector must equal the number of type i points in X.

a function

of the form function(x,y) which can be evaluated to give values of the intensity at any locations.

a fitted point process model

(object of class "ppm", "kppm" or "dppm") whose fitted trend can be used as the fitted intensity. (If update=TRUE the model will first be refitted to the data X before the trend is computed.)

omitted:

if lambdaI is omitted then it will be estimated using a leave-one-out kernel smoother.

If lambdaI is omitted, then it will be estimated using a `leave-one-out' kernel smoother.

Similarly the argument lambdadot should contain estimated values of the intensity of the entire point process. It may be either a pixel image, a numeric vector of length equal to the number of points in X, a function, or omitted.

The argument r is the vector of values for the distance \(r\) at which \(G_{i\bullet}(r)\) should be evaluated. The values of \(r\) must be increasing nonnegative numbers and the maximum \(r\) value must not exceed the radius of the largest disc contained in the window.

References

Cronie, O. and Van Lieshout, M.N.M. (2015) Summary statistics for inhomogeneous marked point processes. Annals of the Institute of Statistical Mathematics DOI: 10.1007/s10463-015-0515-z

See Also

Gdot, Ginhom, Gcross.inhom, Gmulti.inhom.

Examples

  X <- rescale(amacrine)
  if(interactive() && require(spatstat.model)) {
    ## how to do it normally
    mod <- ppm(X ~ marks * x)
    lam <- fitted(mod, dataonly=TRUE)
    lmin <- min(predict(mod)[["off"]]) * 0.9
  } else {
    ## for package testing 
    lam <- intensity(X)[as.integer(marks(X))]
    lmin <- intensity(X)[2] * 0.9
  }
  lamI <- lam[marks(X) == "on"]
  GD <- Gdot.inhom(X, "on", lambdaI=lamI, lambdadot=lam, lambdamin=lmin)