# mcpat.test

##### Monte Carlo Inference of Temporal Changes in Spatial Segregation An approximate Monte Carlo test of temporal changes in a multivariate spatial-temporal point process.

Monte Carlo Inference of Temporal Changes in Spatial Segregation An approximate Monte Carlo test of temporal changes in a multivariate spatial-temporal point process.

- Keywords
- htest

##### Usage

`mcpat.test(pts, marks, t, h, 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 data points.

- t
numeric vector of the associated time-periods.

- h
numeric vector of the bandwidths at which to calculate the cross-validated log-likelihood function pooled over times.

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

- proc
logical, default

`TRUE`

prints the processing messages.

##### Details

The spatial-temporal data are denoted as \((x_i, m_i, t_i)\), where \(x_i\) are the spatial locations, \(m_i\) are the categorical mark sequence numbers, and \(t_i\) are the associated time-periods.

The null hypothesis is that the type-specific probability surfaces are
constant over time-periods, *i.e.*, \(p_k(x, t)=p_k(x)\), for any
\(t\), where \(p_k(x, t)\) are the type-specific probabilities for
\(k\)th category within time-period \(t\).

Each Monte Carlo simulation is sampled from an approximate *true*
type-specific probability surfaces --- the estimated one from the data.
Approximately, the simulated data and the original data are samples from
the same probability distribution under the null hypothesis. See Diggle,
P.J. *et al* (2005) for more details.

##### Value

A list with components

- pvalue
\(p\)-value of the approximate Monte Carlo test.

- ...
copy of

`pts, marks, t, h, ntest`

.

##### References

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*