Diggle et al (1995) K-function test for space-time clustering

The function stKtest wraps functions in package splancs to perform the K-function based Monte Carlo permutation test for space-time clustering (Diggle et al, 1995) for "epidataCS". The implementation is due to Meyer et al. (2016).

Usage

stKtest(object, eps.s = NULL, eps.t = NULL, B = 199,
        cores = 1, seed = NULL, poly = object$W)

# S3 method for class 'stKtest'
plot(x, which = c("D", "R", "MC"),
     args.D = list(), args.D0 = args.D, args.R = list(), args.MC = list(),
     mfrow = sort(n2mfrow(length(which))), ...)

Arguments

object: an object of class "epidataCS".
eps.s, eps.t: numeric vectors defining the spatial and temporal grids of critical distances over which to evaluate the test. The default (NULL) uses equidistant values from 0 to the smallest eps.s/eps.t value in object$events, but not larger than half the observed spatial/temporal domain.
B: the number of permutations.
cores: the number of parallel processes over which to distribute the requested number of permutations.
seed: argument for set.seed to initialize the random number generator such that results become reproducible (also if cores > 1, see plapply).
poly: the polygonal observation region of the events (as an object handled by xylist). The default object$W might not work since package splancs does not support multi-polygons. In this case, the poly argument can be used to specify a substitute.
x: an "stKtest".
which: a character vector indicating which diagnostic plots to produce. The full set is c("D", "D0", "R", "MC"). The special value which = "stdiagn" means to call the associated splancs function stdiagn.
args.D,args.D0,args.R,args.MC: argument lists for the plot functions persp (for "D" and "D0"), plot.default ("R"), and truehist ("MC"), respectively, to modify the default settings. Ignored if which = "stdiagn".
mfrow: par-setting to layout the plots. Ignored for which = "stdiagn" and if set to NULL.
...: ignored (argument of the generic).

Value

an object of class "stKtest" (inheriting from "htest"), which is a list with the following components:

method: a character string indicating the type of test performed.
data.name: a character string naming the supplied object.
statistic: the sum $U$ of the standardized residuals $R(s,t)$.
parameter: the number B of permutations.
p.value: the p-value for the test.
pts: the coordinate matrix of the event locations (for stdiagn.
stK: the estimated K-function as returned by stkhat.
seD: the standard error of the estimated $D(s,t)$ as returned by stsecal.
mctest: the observed and permutation values of the test statistic as returned by stmctest.

The plot-method invisibly returns NULL.

References

Diggle, P. J.; Chetwynd, A. G.; Häggkvist, R. and Morris, S. E. (1995): Second-order analysis of space-time clustering Statistical Methods in Medical Research, 4, 124-136.

Meyer, S., Warnke, I., Rössler, W. and Held, L. (2016): Model-based testing for space-time interaction using point processes: An application to psychiatric hospital admissions in an urban area. Spatial and Spatio-temporal Epidemiology, 17, 15-25. doi:10.1016/j.sste.2016.03.002 . Eprint: https://arxiv.org/abs/1512.09052.

Author

Sebastian Meyer

Examples

if (requireNamespace("splancs")) {
    data("imdepi")
    imdepiB <- subset(imdepi, type == "B")
    mainpoly <- coordinates(imdepiB$W@polygons[[1]]@Polygons[[5]])
    SGRID <- c(10, 25, 50, 100, 150)
    TGRID <- c(1, 7, 14, 21)
    B <- 19  # limited here for speed
     
    imdBstKtest <- stKtest(imdepiB, eps.s = SGRID, eps.t = TGRID, B = B,
                           cores = 2, seed = 1, poly = list(mainpoly))
    print(imdBstKtest)
    plot(imdBstKtest)
}