kernstadapt (version 0.4.0)

separability.test: Separability test for spatio-temporal point processes

Description

Performs a separability test of the first-order intensity function based on a Fisher Monte Carlo test of cell counts.

Usage

separability.test(X, t = NULL, nx = NULL, ny = NULL, nt = NULL, nperm = 1000)

Value

A list with class "htest" containing the following components:

p.value

the approximate p-value of the test.

method

the character string "Separability test based on Fisher's for counting data".

alternative

a character string describing the alternative hypothesis.

data.name

a character string giving the name(s) of the data.

Arguments

X

A spatial point pattern (an object of class ppp) with the spatial coordinates of the observations.

t

A numeric vector of temporal coordinates with equal length to the number of points in X. This gives the time associated with each spatial point.

nx, ny, nt

Numbers of quadrats in the \(x,y\) and \(t\) directions.

nperm

An integer specifying the number of replicates used in the Monte Carlo test.

Author

Jonatan A. González

Details

This function performs a basic test of the separability hypothesis in a manner similar to independence test in two-way contingency tables. The test is conditional on the observed number of points. It considers a regular division of the interval \(T\) into disjoint sub-intervals \(T_1,...,T_{n_t}\) and similarly a division of the window \(W\) into disjoint subsets \(W_1, ..., W{n_x \times n_y}\). Then the function computes Fisher's test statistic and get a p-value based on Monte Carlos approximation.

References

Ghorbani et al. (2021) Testing the first-order separability hypothesis for spatio-temporal point patterns, Computational Statistics & Data Analysis, 161, p.107245.

Examples

data(lGCpp)
separability.test(lGCpp, nx = 5, ny = 4, nt = 3, nperm = 500)

# \donttest{
data(aegiss)
separability.test(aegiss, nx = 8, ny = 8, nt = 4)
# }