spatstat.explore (version 3.1-0)

GmultiInhom: Inhomogeneous Marked G-Function

Description

For a marked point pattern, estimate the inhomogeneous version of the multitype \(G\) function, effectively the cumulative distribution function of the distance from a point in subset \(I\) to the nearest point in subset \(J\), adjusted for spatially varying intensity.

Usage

GmultiInhom(X, I, J,
             lambda = NULL, lambdaI = NULL, lambdaJ = NULL,
             lambdamin = NULL, ...,
             r = NULL,
             ReferenceMeasureMarkSetI = NULL,
             ratio = FALSE)

Value

Object of class "fv" containing the estimate of the inhomogeneous multitype \(G\) function.

Arguments

X

A spatial point pattern (object of class "ppp".

I

A subset index specifying the subset of points from which distances are measured. Any kind of subset index acceptable to [.ppp.

J

A subset index specifying the subset of points to which distances are measured. Any kind of subset index acceptable to [.ppp.

lambda

Intensity estimates for each point of X. A numeric vector of length equal to npoints(X). Incompatible with lambdaI,lambdaJ.

lambdaI

Intensity estimates for each point of X[I]. A numeric vector of length equal to npoints(X[I]). Incompatible with lambda.

lambdaJ

Intensity estimates for each point of X[J]. A numeric vector of length equal to npoints(X[J]). Incompatible with lambda.

lambdamin

A lower bound for the intensity, or at least a lower bound for the values in lambdaJ or lambda[J].

...

Ignored.

r

Vector of distance values at which the inhomogeneous \(G\) function should be estimated. 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.

Author

Ottmar Cronie and Marie-Colette van Lieshout. Rewritten for spatstat by Adrian Baddeley .

Details

See Cronie and Van Lieshout (2015).

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

Ginhom, Gmulti

Examples

  X <- rescale(amacrine)
  I <- (marks(X) == "on")
  J <- (marks(X) == "off")
  if(require(spatstat.model)) {
    mod <- ppm(X ~ marks * x)
    lam <- fitted(mod, dataonly=TRUE)
    lmin <- min(predict(mod)[["off"]]) * 0.9
  } else {
    lam <- intensity(X)[as.integer(marks(X))]
    lmin <- intensity(X)[2] * 0.9
  }
  plot(GmultiInhom(X, I, J, lambda=lam, lambdamin=lmin))
  # equivalent
  plot(GmultiInhom(X, I, J, lambdaI=lam[I], lambdaJ=lam[J], lambdamin=lmin),
       main="")