[R-sig-Geo] R-sig-Geo Digest, Vol 30, Issue 6

[Adrian Baddeley]

Charlotte Reemts writes:

 > I am conducting an analysis on disease spread in oak trees.  I have the
 > locations of symptomatic trees for two years (2004 and 2005) in an
 > irregularly-shaped polygon and want to know whether there is attraction or
 > repulsion between the two years.  The symptomatic trees are clustered within
 > a year.

 > I used Kcross to calculate the K statistic for my data

     First a warning. The usual interpretation of the bivariate K function is
     probably not appropriate in this application.
     It would not be appropriate to draw conclusions by 
     comparing the computed Kcross function with the curve K(r) = pi r^2.
     The trees do not move from year to year (oder?). 
     Presumably it is possible for a given tree to be symptomatic 
     in both years. So the two point patterns may share points in common.
     So the usual assumptions for the bivariate K function are false.
     
 > and would like to calculate simulation/confidence envelopes (for
 > the univariate data, I used Kenv). 

     OK, you can of course do a Monte Carlo test (using the envelopes)

 > I tried using Kenv.label, but based on my reading of the
 > literature, random labelling is not the appropriate test (see
 > Goreaud and Pelissier, 2003, Journal of Vegetation Science).
 > I cannot use Kenv.tor because my study area is not rectangular.

 > Next, I tried using this code:
 > kcross.envelope<-envelope(my.data, Kcross, correction="translate", nsim=99)

 > The result I get is reasonable, but I would like more information on how
 > 'envelope' generates the envelopes (and how it labels the points) and
 > whether this is an appropriate test for my data.

   envelope() is a function in the library `spatstat'. 

   help(envelope) explains that the random patterns used to calculate
   the envelopes are, **by default**, generated from a Poisson process
   with the same intensity as the data point pattern. If the data are
   a marked point pattern, this means that the random patterns are
   realisations of a Poisson MARKED point process - in other words,
   the locations of the points are Poisson (CSR), and their marks are
   independent random marks. The random patterns are
   randomly-labelled, completely random patterns.

   If this default behaviour is not what you want,
   then use the argument 'simulate' (of the envelope() function)
   to specify how you want the random patterns to be generated. 

   For example, if you wanted to randomly relabel the existing data pattern
   without changing the point locations, 

	   envelope(mydata, Kcross, simulate=expression(rlabel(mydata)))

   [Warning: this is in spatstat - be careful of the conflict with the 
   command 'rlabel' in splancs]

   > I cannot use Kenv.tor because my
   > study area is not rectangular.

   Apparently you want to generate envelopes based on randomly shifting
   the existing data pattern (points of each type shifted separately).

   The following will work (in spatstat). 

          rsh <- function(X, d) {
	      W <- X$window
	      B <- bounding.box(W)
	      XB <- X[,B]
	      Y <- rtoro(XB, radius=d)
	      Be <- erode.owin(W, d)
	      Y <- Y[,Be]
	      return(Y)
	      }

          rad <- 25
	  W <- rsh(mydata, rad)$window
	  M <- mydata[,W]

	  envelope(M, Kcross, simulate=expression(rsh(mydata, rad)))

   The new function rsh(X, d) applies random shifts
   to the sub-patterns of points of each type, with a maximum shift
   distance of d units (change this value 'rad' to a reasonable distance
   for your data). It returns a point pattern whose observation window
   has been eroded by a distance of d units. Thus, no toroidal wrapping
   is needed, and this function works even if X has a non-rectangular window.

   The point pattern M is just the restriction of 'mydata' to the 
   same eroded window, so that comparisons of the Kcross values are
   meaningful.

   This will become easier in spatstat 1.9.

HTH
Adrian Baddeley