# mcseg.test

0th

Percentile

##### Monte Carlo Test of Spatial Segregation in Multivariate Point Process

Monte Carlo test of spatial segregation in a multivariate point process by simulating data from random re-labelling of the categorical marks.

Keywords
htest
##### Usage
mcseg.test(pts, marks, h, stpts = NULL, ntest = 100, proc = TRUE)
##### Arguments
pts

matrix containing the x,y-coordinates of the data point locations.

marks

numeric/character vector of the marked type labels of the point pattern.

h

numeric vector of the bandwidths at which to calculate the cross-validated likelihood function.

stpts

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.

ntest

integer with default 100, number of simulations for the Monte Carlo test.

proc

logical with default TRUE to print the processing messages.

##### Details

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.

##### Value

A list with components

pvalue

numeric, $p$-value of the Monte Carlo test.

stpvalue

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.

##### References

1. Kelsall, J. E. and Diggle, P. J. (1998) Spatial variation in risk: a nonparametric binary regression approach, Applied Statistics, 47, 559--573.

2. 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.

cvloglk and phat