mpp.characteristics {MarkedPointProcess}R Documentation

Characteristics of the marks of a marked point process

Description

mpp.characteristics returns summary statistics for the marks of a marked point process

Usage

mpp.characteristics(...,bin=NULL, rep=1, p=0.8, name="", normalize=TRUE,
                    show=FALSE, model=NULL, param=NULL, summarize=TRUE,
                    PrintLevel=RFparameters()$Print,
                    dev=if (name=="") 2 else FALSE,
                    rdline=if (is.logical(dev)) NULL else readline,
                    staticchoice=FALSE)

Arguments

... coordinates and the data for the species, see Details
bin sequence of increasing bin margins for the functions E, V, and S; see Details
rep number of independent measurements of the marks (at each point); usually 1
p in [0,1]; outlier threshold for the robustified distance function of the test statistics
name character; if show=FALSE this parameter is ignored. Otherwise, if name="" then plots are printed on the screen else name is the main name of the postscript files
normalize logical; if TRUE the data are (marginally) transformed to Gaussian variables (for each species, each kind of mark, and each realisation, seperately) before being analysed
show logical; if TRUE the results are also shown graphically
model the variogram model to compare with the mark variogram; see CovarianceFct
param the parameters for the variogram model; see CovarianceFct
summarize logical; if FALSE results are for each realisation seperately (instead of being averaged over the realisations).
PrintLevel 0,1 or 2. The function gives some short messages if PrintLevel is 1 or 2.
rdline NULL or function. if not NULL then the function is called after each plot with a string parameter that gives file or image information
dev the graphical device for the output, see Dev
staticchoice logical. The calculation of some variances requires the splitting of the data into group. If staticchoice=FALSE this is done in a random way. staticchoice=TRUE is only used for internal testing.

Details

bin: analogously to the variogram in geostatistics, the characteristics E, V, and S of a stationary and isotropic marked point process depend on the distance r. Instead of returning a cloud of values, binned values are calculated in the same way the binned variogram is calculated. 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, ...).

...: data for mark point processes typically split up into different species (ill/healthy cells; beaches/oaks/pines); furthermore, multivariate data are measured for each individual (size of the cell; diameter of the stem, height of the tree). The function calculates many cross-statistics; for example the cross variogram of mark A of species B and mark C of species D given species B and species D are a distance r apart.

Denote by S_i species i, i=1,...,s. Due to the potential complexity of the data, the data are passed to mpp.characteristics in the following way:
(coordinates of species S_i), (marks of species A),..., (coordinates of species Z), (marks of species Z)
The coordinates are n_i x 2 matrices; the data are n_i x m x rep matrices, if the data are m-variate, and rep independent observations of the data exist. In case rep>1 the sequence for the data is:
columns 1:m : first set of the m-variate data,...,
columns (m * rep - m + 1) : (m * rep) : last set of the m-variate data.

Note that m and rep must be identical for all species.

The function returns the following values if summarize=TRUE. Denote by M_k(S_i) the kth mark of species S_i, and by d_ij the distance of two indviduals of species S_i and S_j. Denote by s the number of species.

summarize=FALSE : the column structure of the above matrices is rep times repeated.

Value

mpp.characteristics returns list(E, ETest, VAR, VARTest, SQ, SQTest, KMM, GAM, Ebin, VARbin, KMMbin, GAMbin, midbin, call = match.call()); see Details. The return is invisible if show=TRUE.

Author(s)

Martin Schlather, martin.schlather@math.uni-goettingen.de http://www.stochastik.math.uni-goettingen.de/institute

References

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

Schlather, M. (2001) On the second order characteristics of marked point processes, Bernoulli 7, 99-117.

See Also

rfm.test, simulateMPP

Examples

data(BITOEK)

bin <- c(-1, seq(0, 50, 2))
normalize <- TRUE
mpp <- mpp.characteristics(bin=bin, normalize=normalize, show=TRUE,
                   coord=steigerwald$coord, diam=steigerwald$diam)
str(mpp)

[Package MarkedPointProcess version 0.2.9 Index]