
Well, what I called "visual test" is in fact a 
"formal" pointwise Monte Carlo test (Ripley, 
1981). In  words of Baddeley an Turner (help page of  "envelope"):

  "The test is constructed by choosing a fixed 
value of r, and rejecting the null hypothesis if 
the observed function value lies outside the 
envelope at this value of r. This test has exact 
significance level alpha = 2 * nrank/(1 + nsim)",

  i.e., for a choosed r, if the observed K is 
outside the envelopes, reject the CSR hypothesis 
with alpha = 2* 1/(1+99) = 0.02.

Another formal simultaneous or global tests , 
e.g., GoF test in the sense of Diggle (2003:14) 
or Loosmore and Ford (2006), or the simultaneous 
test that Baddeley and Turner describe on the 
help page  of envelope are quite straightforward 
to build from the computed "kobs" and "ksim".


Cheers,

Marcelino


Loosmore, N. B. and Ford, E.D. (2006) Statistical 
Inference Using the G or K Point Pattern Spatial 
Statistics. Ecology 87, 1925-1931

At 18:04 15/03/2010, tobias.verbeke@openanalytics.eu wrote:

>Dear Marcelino,
>
>Many thanks for your prompt response and the
>code for a visual test.
>
>Cressie (1993, p. 635, 639, 642) mentions quite
>some statistics for formal testing in 2D.
>
>In the mean time I tracked already the generalization
>to n dimensions of Pielou's statistic (Cressie, p. 635)
>
>Howard B. Stauffer (1979). A generalization of
>Pielou's index of non-randomness,
>Journal of Theoretical Biology 77 (1), p. 19-25
>
>I will report back to the list if I find others
>(and implemented one).
>
>Thanks again,
>Tobias
>
>On Mon, 15 Mar 2010 15:19:47 +0100, Marcelino de la Cruz
><marcelino.delacruz@upm.es> wrote:
> > A simple MonteCarlo procedure:
> >
> > #sample data:
> > X <- rpoispp3(50)
> >
> >
> > n <- dim(X$data)[1]
> > volume <- volume.box3(as.box3(X))
> >
> > lambda <- n / volume
> >
> >
> > # observed isotropic  corrected K
> > kobs <- K3est(X, rmax=1,nrval=101)$iso
> >
> > #99 simulated CSR patterns
> >
> > Xsim<- vector("list", 99)
> > for  (i in 1: 99){
> >     Xsim[[i]] <- rpoispp3(lambda, domain = as.box3(X))
> > }
> >
> > #simulated K functions
> >   ksim <- sapply(Xsim, function(x) K3est(x, rmax=1,nrval=101)$iso)
> >
> > # "visual CSR test"
> > plot(0:100, kobs, xlab="r", ylab="K3est(r)", type="l")
> > matplot(0:100,t(apply(ksim,1,range)), lty=2,col=2, type="l", add=T)
> >
> > # another one:
> >   plot(0:100, (3*kobs/(4*pi*(0:100)^3)), xlab="r", ylab="L3est(r)",
> >   type="l")
> >   matplot(0:100,(3*t(apply(ksim,1,range))/(4*pi*(0:100)^3)),
> > lty=2,col=2, type="l", add=T)
> >
> > HTH,
> >
> > Marcelino
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> >
> > At 13:29 15/03/2010, tobias.verbeke@openanalytics.eu wrote:
> >
> >>Dear list,
> >>
> >>Is there any functionality available to test
> >>CSR for a three-dimensional point pattern ?
> >>
> >>I am aware there is basic infrastructure for 3D
> >>point patterns in spatstat
> >>
> >> > methods(class = "pp3")
> >>[1] crossdist.pp3  nnclean.pp3    nndist.pp3     nnwhich.pp3
> >>pairdist.pp3
> >>[6] plot.pp3       print.pp3      summary.pp3    unitname<-.pp3
> >>unitname.pp3
> >>
> >>(as well as through rpoispp3, K3est, F3est, G3est), but would appreciate
> >>any hints on possibilities to combine these building blocks
> >>into a test for CSR.
> >>
> >>Pointers to asymptotic results will be appreciated by my computer,
> >>pointers to simple Monte Carlo procedures will be appreciated by
> >>myself..
> >>
> >>Many thanks in advance,
> >>Tobias
> >>
> >>_______________________________________________
> >>R-sig-Geo mailing list
> >>R-sig-Geo@stat.math.ethz.ch
> >>https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> >
> > ________________________________
> >
> > Marcelino de la Cruz Rot
> >
> > Departamento de  BiologÃ­a Vegetal
> > E.U.T.I. AgrÃ­cola
> > Universidad PolitÃ©cnica de Madrid
> > 28040-Madrid
> > Tel.: 91 336 54 35
> > Fax: 91 336 56 56
> > marcelino.delacruz@upm.es
> > _________________________________

________________________________

Marcelino de la Cruz Rot

Departamento de  Biología Vegetal
E.U.T.I. Agrícola
Universidad Politécnica de Madrid
28040-Madrid
Tel.: 91 336 54 35
Fax: 91 336 56 56
marcelino.delacruz@upm.es
_________________________________ 
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