Given temporal and spatial distances as well as corresponding critical
thresholds defining what “close” means, the function
knox performs Knox (1963, 1964) test for space-time interaction.
The corresponding p-value can be calculated either by the Poisson
approximation or by a Monte Carlo permutation approach (Mantel, 1967)
with support for parallel computation via plapply.
There is a simple plot-method showing a truehist of
the simulated null distribution together with the expected and observed
values.
This implementation of the Knox test is due to Meyer et al. (2016).
knox(dt, ds, eps.t, eps.s, simulate.p.value = TRUE, B = 999, ...)# S3 method for knox
plot(x, ...)
an object of class "knox" (inheriting from "htest"),
which is a list with the following components:
a character string indicating the type of test performed, and whether the Poisson approximation or Monte Carlo simulation was used.
a character string giving the supplied dt and
ds arguments.
the number of close pairs.
if simulate.p.value = TRUE, the number
B of permutations, otherwise the lambda parameter of
the Poisson distribution, i.e., the same as null.value.
the p-value for the test. In case
simulate.p.value = TRUE, the p-value from the Poisson
approximation is still attached as an attribute "Poisson".
the character string "greater" (this is a
one-sided test).
the expected number of close pairs in the absence of space-time interaction.
the contingency table of dt <= eps.t and
ds <= eps.s.
The plot-method invisibly returns NULL.
A toLatex-method exists, which generates LaTeX code for the
contingency table associated with the Knox test.
numeric vectors containing temporal and spatial distances, respectively.
Logical vectors indicating temporal/spatial closeness may also be
supplied, in which case eps.t/eps.s is ignored.
To test for space-time interaction in a single point pattern of "dist" objects).
Note that there is no special handling of matrix input, i.e.,
if dt or ds are matrices, all elements are used
(but a warning is given if a symmetric matrix is detected).
Critical distances defining closeness in time and space, respectively. Distances lower than or equal to the critical distance are considered “"close"”.
logical indicating if a Monte Carlo permutation test should be
performed (as per default). Do not forget to set the
.Random.seed via an extra .seed argument if
reproducibility is required (see the ... arguments below).
If simulate.p.value = FALSE, the Poisson approximation is
used (but see the note below).
number of permutations for the Monte Carlo approach.
arguments configuring plapply:
.parallel, .seed, and .verbose.
By default, no parallelization is performed (.parallel = 1),
and a progress bar is shown (.verbose = TRUE).
For the plot-method, further arguments passed to
truehist.
an object of class "knox" as returned by the
knox test.
Sebastian Meyer
Knox, G. (1963): Detection of low intensity epidemicity: application to cleft lip and palate. British Journal of Preventive & Social Medicine, 17, 121-127.
Knox, E. G. (1964): The detection of space-time interactions. Journal of the Royal Statistical Society. Series C (Applied Statistics), 13, 25-30.
Kulldorff, M. and Hjalmars, U. (1999): The Knox method and other tests for space-time interaction. Biometrics, 55, 544-552.
Mantel, N. (1967): The detection of disease clustering and a generalized regression approach. Cancer Research, 27, 209-220.
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. tools:::Rd_expr_doi("10.1016/j.sste.2016.03.002"). Eprint: https://arxiv.org/abs/1512.09052.
The function mantel.randtest in package ade4
implements Mantel's (1967) space-time interaction test, i.e., using
the Pearson correlation between the spatial and temporal distances of
all event pairs as the test statistic, and assessing statistical
significance using a Monte Carlo permutation approach as with
simulate.p.value here in the knox function.
To combine information from different scales eps.t and
eps.s while also handling edge effects, the space-time
K-function test available via stKtest can be used.
Function epitest tests epidemicity in a
"twinstim" point process model.
data("imdepi")
imdepiB <- subset(imdepi, type == "B")
## Perfom the Knox test using the Poisson approximation
knoxtest <- knox(
dt = dist(imdepiB$events$time), eps.t = 30,
ds = dist(coordinates(imdepiB$events)), eps.s = 50,
simulate.p.value = FALSE
)
knoxtest
## The Poisson approximation works well for these data since
## the proportion of close pairs is rather small (204/56280).
.opt <- options(xtable.comment = FALSE)
## contingency table in LaTeX
toLatex(knoxtest)
options(.opt)
## Obtain the p-value via a Monte Carlo permutation test,
## where the permutations can be computed in parallel
## (using forking on Unix-alikes and a cluster on Windows, see ?plapply)
knoxtestMC <- knox(
dt = dist(imdepiB$events$time), eps.t = 30,
ds = dist(coordinates(imdepiB$events)), eps.s = 50,
simulate.p.value = TRUE, B = 99, # limited here for speed
.parallel = 2, .seed = 1, .verbose = FALSE
)
knoxtestMC
plot(knoxtestMC)
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