globaldiag {stopp}

Global diagnostics of a spatio-temporal point process first-order intensity

Description

This function performs global diagnostics of a model fitted for the first-order intensity of a spatio-temporal point pattern, by returning the inhomogeneous K-function weighted by the provided intensity to diagnose, its theoretical value, and their difference.

Usage

globaldiag(x, intensity)

Arguments

x

A stp object

intensity

A vector of intensity values, of the same length as the number of point in x

Details

If applied to a stp object, it resorts to the spatio-temporal inhomogeneous K-function (Gabriel and Diggle, 2009) documented by the function STIKhat of the stpp package (Gabriel et al, 2013).

If applied to a stlp object, it uses the spatio-temporal inhomogeneous K-function on a linear network (Moradi and Mateu, 2020) documented by the function STLKinhom of the stlnpp package (Moradi et al., 2020).

Value

A list of class globaldiag, containing

x

The observed point pattern

dist

The spatial ranges of the K-function

times

The temporal ranges of the K-function

est

The estimated K-function weighted by the intensity function in input

theo

The theoretical K-function

diffK

The difference between the estimated and the theoretical K-functions

squared.diff

The sum of the squared differences between the estimated and the theoretical K-functions

Author(s)

Nicoletta D'Angelo and Giada Adelfio

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. (2022) Local inhomogeneous second-order characteristics for spatio-temporal point processes on linear networks. Stat Papers. https://doi.org/10.1007/s00362-022-01338-4

Gabriel, E., and Diggle, P. J. (2009). Second‐order analysis of inhomogeneous spatio‐temporal point process data. Statistica Neerlandica, 63(1), 43-51.

Gabriel, E., Rowlingson, B. S., & 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

Moradi M, Cronie O, and Mateu J (2020). stlnpp: Spatio-temporal analysis of point patterns on linear networks.

Moradi, M. M., and Mateu, J. (2020). First-and second-order characteristics of spatio-temporal point processes on linear networks. Journal of Computational and Graphical Statistics, 29(3), 432-443.

See Also

plot.globaldiag, print.globaldiag, summary.globaldiag

Examples

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, par = c(.3, 6))

mod1 <- stppm(inh, formula = ~ 1)
mod2 <- stppm(inh, formula = ~ x)

g1 <- globaldiag(inh, mod1$l)
g2 <- globaldiag(inh, mod2$l)