rfm.test {MarkedPointProcess}R Documentation

MC test on random field model

Description

rfm.test performs MC tests which enables the user to decide whether a marked point process may be considered as a random field model, i.e., as a model where the marks are independent of the locations

Usage

rfm.test(coord=NULL, data, normalize=TRUE, MCrepetitions=99,  
         MCmodel=list(model="exponential",
           param=c(mean=0,variance=NA,nugget=0,scale=NA)),
         method=NULL,
         bin=c(-1,seq(0,1.2,l=15)), Ebin=seq(0,1,0.01),
         MCregister=1, n.hypo=1000,
         pvalue=c(90, 95, 99), tests="l1 & w3",
         tests.lp=NULL, tests.weight=NULL, Barnard=FALSE,
         PrintLevel=RFparameters()$Print,...
         )

Arguments

coord matrix with 2 columns; the coordinates of the pointss
data vector or matrix; the univariate marks that correspond to the locations; if data is a matrix then each column is interpreted as an independent observation given the locations coord; see Details for further possibilities
normalize logical; if TRUE the data are transformed to standard normal data before analysed; if data is a matrix this is done for each column separately
MCrepetitions usually 19 or 99; number of simulations that are compared with the data
MCmodel variogram model to be fitted, see fitvario.
method method used to simulate Gaussian random fieldsl; see GaussRF
bin sequence of increasing bin margins for calculating the function E, V, etc; see Details
Ebin sequence of increasing bin margins for the resulting relative MC test positions of the data; see Details
MCregister 0:9; the register to which intermediate results are stored when the random fields are generated for the MC test
n.hypo number of repeated MC tests, see Details
pvalue test levels
tests vector of characters, see Details.
tests.lp vector of characters, see Details.
tests.weight vector of characters, see Details.
Barnard test by Barnard (1963) on the independence of marks
PrintLevel If zero
... any parameter for variofit can be passed, except for x, y, z, T, data, model, param, mle.methods and cross.methods

Details

data: there are three possibilities to pass the data

bin: as the variogram in geostatistics, the characteristics for the marks of a marked point process depend on a distance (vector) r. Instead of returning a cloud of values, binned values are calculated in the same way the binned variogram is obtained. bin gives the margins of the bins (left open, right closed ones) as an increasing sequence. The first bin must include the zero, i.e., bin=c(-1, 0, ...).

Ebin is ignored if only a single realisation of the data is given. Otherwise Ebin gives the bounds of the bins for the calculated test statistics.

n.hypo : the testing algorithm for a data set is as follows:

tests, tests.lp, tests.weight:

Value

list(E=,VAR=,SQ=,M=,est=,...) where ... are the input parameters such as normalize, MCrepetitions, MCmodel, MCparam, sill, bin, Ebin. Let n be the number of currently implemented versions of the MC test (using different weights and lp-norms). Then VAR, SQ, and M are all matrices with n columns. The number of rows depends on the input parameters: If only one realisation of the data is given then the absolute test positions of the MC test is returned in E, VAR, SQ, and M in a single row. If several realisations of the data (and the coord) are given, then the number of rows equals length(Ebin)-1, and the each entry contains the number of statistics falling into respective (relative) bin given by Ebin.

Author(s)

Martin Schlather, schlath@hsu-hh.de http://www.unibw-hamburg.de/WWEB/math/schlath/schlather.html

References

Barnard, G. (1963) Discussion paper to M.S. Barlett on “The spectral analysis of point processes”, J. R. Statist. Soc. Ser. B, 25, 294.

Besag, J. and Diggle, P. (1977) Simple Monte Carlo tests for spatial pattern. J. R. Statist. Soc. Ser. C, 26, 327–333.

Schlather, M., Ribeiro, P. and Diggle, P. (2004) Detecting Dependence Between Marks and Locations of Marked Point Processes J. R. Statist. Soc., Ser. B 66, 79-83.

See Also

mpp.characteristics, simulate.mpp

Examples






[Package MarkedPointProcess version 0.1.4 Index]