spatstat.explore (version 3.2-3)

Jmulti.inhom: Inhomogeneous Marked J-Function

Description

For a marked point pattern, estimate the inhomogeneous version of the multitype \(J\) function.

Usage

Jmulti.inhom(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 \(J\) function.

Arguments

X

The observed point pattern, from which an estimate of the inhomogeneous multitype \(J\) function \(J_{IJ}(r)\) will be computed. It must be a marked point pattern. See under Details.

I

Subset index specifying the points of X from which distances are measured, for the inhomogeneous \(G\) function.

J

Subset index specifying the points in X to which distances are measured, for the inhomogeneous \(G\) and \(F\) functions.

lambda

Optional. Values of the estimated intensity function. Either a vector giving the intensity values at the points of the pattern X, a pixel image (object of class "im") giving the intensity values at all locations, a fitted point process model (object of class "ppm") or a function(x,y) which can be evaluated to give the intensity value at any location.

lambdaI

Optional. Values of the estimated intensity of the sub-process X[I]. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the points in X[I], 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,

lambdaJ

Optional. Values of the estimated intensity of the sub-process X[J]. Either a pixel image (object of class "im"), a numeric vector containing the intensity values at each of the points in X[J], 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.

...

Extra arguments passed to as.mask to control the pixel resolution for the computation.

r

vector of values for the argument \(r\) at which the inhomogeneous \(K\) function 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.

Author

Jonatan Gonzalez and Adrian Baddeley .

Details

This function is the counterpart of Jmulti for inhomogeneous patterns. It is computed by evaluating the inhomogeneous \(G\) function GmultiInhom and the inhomogeneous \(F\) function FmultiInhom and computing the ratio \(J = (1-G)/(1-F)\).

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

Jcross.inhom, Jdot.inhom for special cases.

GmultiInhom, FmultiInhom, Jmulti.

Examples

  X <- rescale(amacrine)
  I <- (marks(X) == "on")
  J <- (marks(X) == "off")
  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
    dd <- NULL
  } else {
    ## for package testing
    lam <- intensity(X)[as.integer(marks(X))]
    lmin <- intensity(X)[2] * 0.9
    dd <- 32
  }
  JM <- Jmulti.inhom(X, I, J, lambda=lam, lambdamin=lmin, dimyx=dd)