Perform a Monte-Carlo test of space-time clustering.
stmctest(pts, times, poly, tlimits, s, tt, nsim, quiet=FALSE, returnSims=FALSE)
- A set of points as used by Splancs.
A vector of times, the same length as the number of points in
- A polygon enclosing the points.
- A vector of length 2, specifying the upper and lower temporal domain.
- A vector of spatial distances for the analysis.
- A vector of times for the analysis.
- The number of simulations to do.
quiet=TRUEthen no output is produced, otherwise the function prints the number of simulations completed so far, and also how the test statistic for the data ranks with the simulations.
- default FALSE, if TRUE, return the
stkhatoutput for the observed data and each simulation as attributes
The function uses a sum of residuals as a test statistic, randomly permutes the times of the set of points and recomputes the test statistic for a number of simulations. See Diggle, Chetwynd, Haggkvist and Morris (1995) for details.
A list with components:
nsimvalues each of which is a simulated value of the statistic
The example of using returned simulated values is included only to show how the values might be used, not to indicate that this constitutes a way of examining which observed values of the space-time measure are exceptional.
Diggle, P., Chetwynd, A., Haggkvist, R. and Morris, S. 1995 Second-order analysis of space-time clustering. Statistical Methods in Medical Research, 4, 124-136;Bailey, T. C. and Gatrell, A. C. 1995, Interactive spatial data analysis. Longman, Harlow, pp. 122-125; Rowlingson, B. and Diggle, P. 1993 Splancs: spatial point pattern analysis code in S-Plus. Computers and Geosciences, 19, 627-655; the original sources can be accessed at: http://www.maths.lancs.ac.uk/~rowlings/Splancs/. See also Bivand, R. and Gebhardt, A. 2000 Implementing functions for spatial statistical analysis using the R language. Journal of Geographical Systems, 2, 307-317.
example(stkhat) bur1mc <- stmctest(burpts, burkitt$t, burbdy, c(400, 5800), seq(1,40,2), seq(100, 1500, 100), nsim=49, quiet=TRUE, returnSims=TRUE) plot(density(bur1mc$t), xlim=range(c(bur1mc$t0, bur1mc$t))) abline(v=bur1mc$t0) r0 <- attr(bur1mc, "obs")$kst-outer(attr(bur1mc, "obs")$ks, attr(bur1mc, "obs")$kt) rsimlist <- lapply(attr(bur1mc, "sims"), function(x) x$kst - outer(x$ks, x$kt)) rarray <- array(do.call("cbind", rsimlist), dim=c(20, 15, 49)) rmin <- apply(rarray, c(1,2), min) rmax <- apply(rarray, c(1,2), max) r0 < rmin r0 > rmax