R: Monte-Carlo test of space-time clustering

stmctest {splancs} | R Documentation

## Monte-Carlo test of space-time clustering

### Description

Perform a Monte-Carlo test of space-time clustering.

### Usage

    stmctest(pts, times, poly, tlimits, s, tt, nsim, quiet=FALSE, returnSims=FALSE)

### Arguments

`pts` | A set of points as used by Splancs.
`times` | A vector of times, the same length as the number of points in `pts`.
`poly` | A polygon enclosing the points.
`tlimits` | A vector of length 2, specifying the upper and lower temporal domain.
`s` | A vector of spatial distances for the analysis.
`tt` | A vector of times for the analysis.
`nsim` | The number of simulations to do.
`quiet` | If `quiet=TRUE` then 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.
`returnSims` | default FALSE, if TRUE, return the `stkhat` output for the observed data and each simulation as attributes `obs` and `sims`

### Details

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.

### Value

A list with components:

`t0` | The observed value of the statistic
`t` | A single column matrix with `nsim` values each of which is a simulated value of the statistic

### Note

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.

### References

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: https://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.

### See Also

`stkhat`, `stsecal`, `stvmat`, `stdiagn`

### Examples

    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

[Package splancs version 2.01-43 Index]