Monte Carlo test of spatial segregation in a multivariate point process by simulating data from random re-labelling of the categorical marks.
mcseg.test(pts, marks, h, stpts = NULL, ntest = 100, proc = TRUE)matrix containing the x,y-coordinates of the data point
locations.
numeric/character vector of the marked type labels of the point pattern.
numeric vector of the bandwidths at which to calculate the cross-validated likelihood function.
matrix containing the x,y-coordinates of the locations at
which to implement the pointwise segregation test, with default NULL
not to do the pointwise segregation test.
integer with default 100, number of simulations for the Monte Carlo test.
logical with default TRUE to print the processing
messages.
A list with components
numeric, \(p\)-value of the Monte Carlo test.
matrix, \(p\)-values of the test at each point in
stpts (if stpts is not NULL), with each column corresponds
to one type
copy of the arguments pts, marks, h, stpts, ntest, proc.
The null hypothesis is that the estimated risk surface is spatially
constant, i.e., the type-specific probabilities are
\(p_k(x)=p_k\), for all \(k\), see phat. Each Monte Carlo
simulation is done by relabeling the data categorical marks at random
whilst preserving the observed number of cases of each type.
The segregation test can also be done pointwise, usually at a fine grid of points, to mark the areas where the estimated type-specific probabilities are significantly greater or smaller than the spatial average.
Kelsall, J. E. and Diggle, P. J. (1998) Spatial variation in risk: a nonparametric binary regression approach, Applied Statistics, 47, 559--573.
Diggle, P. J. and Zheng, P. and Durr, P. A. (2005) Nonparametric estimation of spatial segregation in a multivariate point process: bovine tuberculosis in Cornwall, UK. J. R. Stat. Soc. C, 54, 3, 645--658.