SepTest (version 0.0.1)

chi2.test: Chi-squared test for first-order separability of a spatio-temporal point process

Description

Performs a chi-squared test for testing first-order separability of a spatio-temporal point process. Two procedures are available:

"pure_per"

Classical asymptotic chi-squared test of independence on a space--time count table.

"block_per"

Monte Carlo permutation test based on block-wise permutations of the time component.

Usage

chi2.test(
  X,
  sim.procedure = c("pure_per", "block_per"),
  nblocks = 5L,
  nperm = 199L,
  n.time = 2L,
  n.space = 3L,
  t.region = c(0, 1),
  s.region = c(0, 1, 0, 1)
)

Value

Numeric scalar: the p-value of the test.

Arguments

X

A numeric matrix or data frame with at least three columns giving event coordinates \((x, y, t)\).

sim.procedure

Character string specifying the procedure: "pure_per" or "block_per".

nblocks

Integer (>= 2). Number of temporal blocks used for block permutation (only for "block_per").

nperm

Integer (>= 1). Number of Monte Carlo permutations (only for "block_per").

n.time

Integer (>= 2). Number of temporal intervals in the contingency table.

n.space

Integer (>= 2). The spatial domain is partitioned into n.space bins per axis (yielding n.space^2 spatial cells) for the contingency table.

t.region

Numeric vector of length 2 giving the temporal window c(tmin, tmax) with tmin < tmax.

s.region

Spatial window specification. By default, the bounding box c(0, 1, 0, 1) corresponding to c(xmin, xmax, ymin, ymax). Passed to chisq.test.stPP.

Author

Mohammad Ghorbani
Nafiseh Vafaei

Details

The classical procedure ("pure_per") applies a chi-squared test of independence to the n.space^2 by n.time contingency table of counts.

The permutation procedure ("block_per") generates up to nperm block-permuted datasets under the null using sim.procedures with method = "block", recomputes the chi-squared statistic for each, and returns a Monte Carlo p-value computed as \((1 + \#\{T_i \ge T_{obs}\})/(nperm + 1)\).

References

Ghorbani M., Vafaei N., Dvořák J., Myllymäki M. (2021). Testing the first-order separability hypothesis for spatio-temporal point patterns. Computational Statistics and Data Analysis, 161, 107245.

Ghorbani, M., Vafaei, N. and Myllymäki, M. (2025). A kernel-based test for the first-order separability of spatio-temporal point processes, TEST.

See Also

chisq.test.stPP, sim.procedures, block.permut

Examples

set.seed(124)
lambda <- get.lambda.function(N = 200, g = 50, model = 4)
Lmax <- get.lambda.max(N = 200, g = 50, model = 4)
X <- rstpoispp(lambda, Lmax)


# Classical chi-squared test
chi2.test(X, sim.procedure = "pure_per", n.time = 2, n.space = 3)

# Monte Carlo permutation test with blocks
chi2.test(X, sim.procedure = "block_per", nblocks = 5, nperm = 100)