Monte Carlo Inference of Temporal Changes in Spatial Segregation An approximate Monte Carlo test of temporal changes in a multivariate spatial-temporal point process.
mcpat.test(pts, marks, t, h, 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 data points.
numeric vector of the associated time-periods.
numeric vector of the bandwidths at which to calculate the cross-validated log-likelihood function pooled over times.
integer with default 100, number of simulations for the Monte Carlo test
logical, default TRUE prints the processing
messages.
A list with components
\(p\)-value of the approximate Monte Carlo test.
copy of pts, marks, t, h, ntest.
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.
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.