# mcseg.test

##### 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

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.

##### See Also

*Documentation reproduced from package spatialkernel, version 0.4-23, License: CC BY-NC-SA 4.0*