Mantel's space-time test

The Pearson correlation, over all pairs of events, between their spatial dissimilarity (the distance, or 1 / (distance + cs) when cs > 0, Mantel's reciprocal transform) and their temporal one (|t_i - t_j|, or 1 / (|t_i - t_j| + ct)), with a permutation test that permutes the times over the fixed locations (Mantel 1967). Drawing distances and intervals independently instead, as some descriptions do, does not keep the dependence among the pairs of one distance matrix and gives no test of stated size. Memory grows with the number of events, not pairs; time with pairs times permutations.

Usage

mantst(
  x,
  y = NULL,
  t,
  cs = 0,
  ct = 0,
  nsim = 999,
  seed = NULL,
  metric = "euclid",
  lonlat = FALSE
)

Arguments

x, y

The points: x and y numeric vectors of equal length; or x a matrix or data frame with columns named x and y (or X and Y, as sf::st_coordinates() names them, or lon and lat with lonlat = TRUE) and y NULL; or x an sf or sfc object of POINT geometries, whose coordinate reference system must agree with lonlat. An unnamed two-column matrix is read as x then y; other columns are never taken by position. Vectors given separately (x, y, and w or t where a function takes them) are matched by name when every one is named and no name repeats, as elsewhere in the package; otherwise by position. No missing or infinite values.

t

The time of each event: finite numbers (for dates, as.numeric() of them, in days or seconds).

cs, ct

The constants of the reciprocal transforms: numbers from 0 (0 uses the raw distance or interval).

nsim

The number of permutations: one whole number from 0.

seed

NULL to draw the simulations' seed from R's generator (so set.seed() fixes them), or one whole number from 0.

metric

The spatial distance: "euclid" or "manhattan"; the test permutes times and needs no expectation, so both are exact.

lonlat

FALSE (the default) when x and y are planar coordinates in one length unit; TRUE when they are longitude and latitude in degrees, which are then projected to metres by eqproj() about their own centre, and centres are returned in degrees. It is never guessed.

Value

A named numeric vector: r (the correlation), pairs, and the permutation p-values pup ((1 + #{r_perm >= r}) / (nsim + 1), large r: events close in space are close in time when both are raw distances), plo (r_perm <= r) and p2 (|r_perm| >= |r|); NaN without permutations. 3 to 46340 events.

References

Mantel, N. (1967). The detection of disease clustering and a generalized regression approach. Cancer Research, 27(2), 209-220.

Examples

set.seed(1)
x <- runif(60)
y <- runif(60)
mantst(x, y, t = x + rnorm(60, sd = 0.1), nsim = 199, seed = 1)
#>           r       pairs         pup         plo          p2 
#>    0.574889 1770.000000    0.005000    1.000000    0.005000