localtest {stopp}

Test of local structure for spatio-temporal point processes

Description

This function performs the permutation test of the local structure for spatio-temporal point pattern data, proposed in Siino et al. (2018), as well as for spatio-temporal point pattern data occurring on the same linear network, following D'Angelo et al. (2021).

Usage

localtest(X, Z, method = c("K", "g"), k, alpha = 0.05, verbose = TRUE)

Arguments

X

Background spatio-temporal point pattern. Usually, the most clustered between X and Z. Must be either a stp or stlp object.

Z

Other spatio-temporal point pattern. Must also be of the same class as X.

method

Character string indicating which version of LISTA function to use: either "K" or "g". If "K", the local spatio-temporal K-function is used to run the test. If "g", the local spatio-temporal pair correlation function is used.

k

Number of permutations

alpha

Significance level

verbose

If TRUE (default) the progress of the test is printed

Details

The test detects local differences between \textbf{x} and \textbf{z} occurring on the same space-time region.

The test ends providing a vector p of p- values, one for each point in \textbf{x}.

If the test is performed for spatio-temporal point patterns as in Siino et al. (2018), that is, on an object of class stp, the LISTA functions \hat{L}^{(i)} employed are the local functions of Adelfio et al. (2020), documented in KLISTAhat and LISTAhat of the stpp package (Gabriel et al, 2013).

If the function is applied to a stlp object, that is, on two spatio-temporal point patterns observed on the same linear network L, the LISTA function \hat{L}^{(i)} used are the ones proposed in D'Angelo et al. (2021), documented in localSTLKinhom and localSTLginhom.

Details on the performance of the test are found in Siino et al. (2018) and D'Angelo et al. (2021), for Euclidean and network spaces, respectively.

Value

A list of class localtest, containing

p

A vector of p-values, one for each of the points in X

X

The background spatio-temporal point pattern given in input

Z

The alternative spatio-temporal point pattern given in input

alpha

The threshold given in input

Xsig

A stp object storing the resulting significant points

Xnosig

A stp object storing the resulting non-significant points

id

The ids of the resulting significant points

Author(s)

Nicoletta D'Angelo and Marianna Siino

References

Adelfio, G., Siino, M., Mateu, J., and Rodríguez-Cortés, F. J. (2020). Some properties of local weighted second-order statistics for spatio-temporal point processes. Stochastic Environmental Research and Risk Assessment, 34(1), 149-168.

D’Angelo, N., Adelfio, G., and Mateu, J. (2021). Assessing local differences between the spatio-temporal second-order structure of two point patterns occurring on the same linear network. Spatial Statistics, 45, 100534.

Gabriel, E., Rowlingson, B. S., and Diggle, P. J. (2013). stpp: An R Package for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns. Journal of Statistical Software, 53(2), 1–29. https://doi.org/10.18637/jss.v053.i02

Siino, M., Rodríguez‐Cortés, F. J., Mateu, J. ,and Adelfio, G. (2018). Testing for local structure in spatiotemporal point pattern data. Environmetrics, 29(5-6), e2463.

See Also

print.localtest, summary.localtest, plot.localtest

Examples

set.seed(2)
X <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)},
            par = c(.005, 5))
Z <- rstpp(lambda = 30)

test <- localtest(X, Z, method = "K", k = 3)