# mcpat.test

0th

Percentile

##### 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

1. 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, phat, mcseg.test