[R-sig-Geo] test for CSR in three dimensions

[tobias.verbeke at openanalytics.eu]

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 at 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
> 
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> 
> At 13:29 15/03/2010, tobias.verbeke at 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 at stat.math.ethz.ch
>>https://stat.ethz.ch/mailman/listinfo/r-sig-geo
> 
> ________________________________
> 
> 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 at upm.es
> _________________________________