Title:	Spatio-Temporal Point Pattern Methods, Model Fitting, Diagnostics, Simulation, Local Tests
Version:	1.0.0
Date:	2025-08-07
Type:	Package
Description:	Toolbox for different kinds of spatio-temporal analyses to be performed on observed point patterns, following the growing stream of literature on point process theory. This R package implements functions to perform different kinds of analyses on point processes, proposed in the papers (Siino, Adelfio, and Mateu 2018<doi:10.1007/s00477-018-1579-0>; Siino et al. 2018<doi:10.1002/env.2463>; Adelfio et al. 2020<doi:10.1007/s00477-019-01748-1>; D’Angelo, Adelfio, and Mateu 2021<doi:10.1016/j.spasta.2021.100534>; D’Angelo, Adelfio, and Mateu 2022<doi:10.1007/s00362-022-01338-4>; D’Angelo, Adelfio, and Mateu 2023<doi:10.1016/j.csda.2022.107679>). The main topics include modeling, statistical inference, and simulation issues on spatio-temporal point processes on Euclidean space and linear networks. Version 1.0.0 has been updated for accompanying the journal publication D Angelo and Adelfio 2025 <doi:10.18637/jss.v113.i10>.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
Depends:	R (≥ 4.1.0)
Imports:	stats, graphics, KernSmooth, MASS, fields, optimx, plot3D, sparr, spatstat.explore, spatstat.geom, spatstat.linnet, spatstat.random, splancs, spatstat.model, spatstat.utils, stlnpp, stpp, mgcv, spatstat.univar
LazyData:	true
Author:	Nicoletta D'Angelo [aut, cre], Giada Adelfio [aut]
Maintainer:	Nicoletta D'Angelo <nicoletta.dangelo@unipa.it>
RoxygenNote:	7.3.2
Config/testthat/edition:	3
NeedsCompilation:	no
Repository:	CRAN
Packaged:	2025-07-08 16:40:21 UTC; Nicoletta
Date/Publication:	2025-07-08 21:50:02 UTC

Spatio-Temporal Point Pattern Methods, Model Fitting, Diagnostics, Simulation, Local Tests

Description

Toolbox for different kinds of spatio-temporal analyses to be performed on observed point patterns, following the growing stream of literature on point process theory. This R package implements functions to perform different kinds of analyses on point processes, proposed in the papers: Siino, Adelfio, and Mateu (2018), Siino et al. (2018), Adelfio et al. (2020), D’Angelo, Adelfio, and Mateu (2021), D’Angelo, Adelfio, and Mateu (2022), and D’Angelo, Adelfio, and Mateu (2023). The main topics include modeling, statistical inference, and simulation issues on spatio-temporal point processes on Euclidean space and linear networks.

Author(s)

Nicoletta D'Angelo [aut,cre] nicoletta.dangelo@unipa.it, Giada Adelfio [aut]

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.

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

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Siino, M., Adelfio, G., and Mateu, J. (2018). Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes. Stochastic environmental research and risk assessment, 32(12), 3525-3539.

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.

Rescaled roads of Chicago (Illinois, USA)

Description

A linear network of class linnet of the roads of Chicago (Illinois, USA) close to the University of Chicago. The window has been rescaled to be enclosed in a unit square.

Usage

data(chicagonet)

Format

A linear network of class linnet

Author(s)

Nicoletta D'Angelo

References

Ang, Q.W., Baddeley, A. and Nair, G. (2012) Geometrically corrected second-order analysis of events on a linear network, with applications to ecology and criminology. Scandinavian Journal of Statistics 39, 591–617.

Examples

data(chicagonet)

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

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)

Catalog of Greek earthquakes

Description

A dataset in stp format containing the catalog of Greek earthquakes of magnitude at least 4.0 from year 2005 to year 2014. Data come from the Hellenic Unified Seismic Network (H.U.S.N.).

Usage

data(greececatalog)

Format

A stp object for a spatio-temporal point pattern with 1111 points

Details

The variables are as follows:

• x. longitude, ranging from 20.02 to 27.98

• y. latitude, ranging from 33.75 to 40.45

• t. time, ranging from 38354, 42000

Author(s)

Nicoletta D'Angelo

References

D’Angelo, N., Siino, M., D’Alessandro, A., and Adelfio, G. (2022). Local spatial log-Gaussian Cox processes for seismic data. AStA Advances in Statistical Analysis, 1-39.

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Gabriel, E., Rodriguez-Cortes, F., Coville, J., Mateu, J., and Chadoeuf, J. (2022). Mapping the intensity function of a non-stationary point process in unobserved areas. Stochastic Environmental Research and Risk Assessment, 1-17.

Siino, M., Adelfio, G., Mateu, J., Chiodi, M., and D’alessandro, A. (2017). Spatial pattern analysis using hybrid models: an application to the Hellenic seismicity. Stochastic Environmental Research and Risk Assessment, 31(7), 1633-1648.

Examples

data(greececatalog)

plot(greececatalog)

Display outlying LISTA functions

Description

This function works on the objects of class localdiag, as returned by localdiag, plotting the identified 'outlying' LISTA functions. These correspond to the influential points in the fitting of the model provided by localdiag

Usage

infl(x, id = NULL)

Arguments

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

See Also

localdiag, plot.localdiag, print.localdiag, summary.localdiag

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)

resmod1 <- localdiag(inh, mod1$l, p = .9)

infl(resmod1)

Local inhomogeneous Spatio-temporal K-functions on a linear network

Description

The functions localSTLKinhom and localSTLginhom implement the inhomogeneous LISTA functions proposed in D'Angelo et al. (2022).

Usage

localSTLKinhom(
  x,
  lambda = lambda,
  normalize = FALSE,
  r = NULL,
  t = NULL,
  nxy = 10
)

Arguments

Details

The homogeneous K-function and pair correlation functions, in D'Angelo et al. (2021), can be obtained easily with localSTLKinhom and localSTLginhom, by imputing a lambda vector of constant intensity values, the same for each point.

Value

A list of class lista. The objects are of class sumstlpp (Moradi and Mateu, 2020).

Author(s)

Nicoletta D'Angelo

References

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.

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

See Also

localSTLginhom, STLKinhom, STLginhom

Examples

set.seed(2)
df_net <- data.frame(x = runif(25, 0, 0.85), y = runif(25, 0, 0.85), t = runif(25))
stlp1 <- stp(df_net, L = chicagonet)
lambda <- rep(diff(range(stlp1$df$x)) * diff(range(stlp1$df$y))
 * diff(range(stlp1$df$t)) / spatstat.geom::volume(stlp1$L),
nrow(stlp1$df))

k <- localSTLKinhom(stlp1, lambda = lambda, normalize = TRUE)

Local inhomogeneous Spatio-temporal pair correlation functions on a linear network

Description

The functions localSTLKinhom and localSTLginhom implement the inhomogeneous LISTA functions proposed in D'Angelo et al. (2022).

Usage

localSTLginhom(x, lambda, normalize = FALSE, r = NULL, t = NULL, nxy = 10)

Arguments

Details

The homogeneous K-function and pair correlation functions, in D'Angelo et al. (2021), can be obtained easily with localSTLKinhom and localSTLginhom, by imputing a lambda vector of constant intensity values, the same for each point.

Value

A list of class lista. The objects are of class sumstlpp (Moradi and Mateu, 2020).

Author(s)

Nicoletta D'Angelo

References

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.

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

See Also

localSTLginhom, STLKinhom, STLginhom

Examples

set.seed(2)
df_net <- data.frame(x = runif(25, 0, 0.85), y = runif(25, 0, 0.85), t = runif(25))
stlp1 <- stp(df_net, L = chicagonet)
lambda <- rep(diff(range(stlp1$df$x)) * diff(range(stlp1$df$y)) 
* diff(range(stlp1$df$t)) / spatstat.geom::volume(stlp1$L),
nrow(stlp1$df))

g <- localSTLginhom(stlp1, lambda = lambda, normalize = TRUE)

Local diagnostics of spatio-temporal point process models

Description

This function performs local diagnostics of a model fitted for the first-order intensity of a spatio-temporal point pattern, returning the points identified as outlying following the diagnostics procedure on individual points of an observed point pattern, as introduced in Adelfio et al. (2020), and applied in D'Angelo et al. (2022) for the linear network case.

The points resulting from the local diagnostic procedure provided by this function can be inspected via the plot, print, summary, and infl functions.

Usage

localdiag(x, intensity, p = 0.95)

Arguments

Details

This function performs local diagnostics of a model fitted for the first-order intensity of a spatio-temporal point pattern, by means of the local spatio-temporal inhomogeneous K-function (Adelfio et al, 2020) documented by the function KLISTAhat of the stpp package (Gabriel et al, 2013).

The function can also perform local diagnostics of a model fitted for the first-order intensity of an spatio-temporal point pattern on a linear network, by means of the local spatio-temporal inhomogeneous K-function on linear networks (D'Angelo et al, 2021) documented by the function localSTLKinhom.

In both cases, it returns the points identified as outlying following the diagnostics procedure on individual points of an observed point pattern, as introduced in Adelfio et al. (2020), and applied in D'Angelo et al. (2022) for the linear network case.

This function computes discrepancies by means of the \chi_i^2 values, obtained following the expression

\chi_i^2=\int_L \int_T \Bigg( \frac{\big(\hat{K}^i_{I}(r,h)- \mathbb{E}[\hat{K}^i(r,h) ] \big)^2}{\mathbb{E}[\hat{K}^i(r,h) ]} \Bigg) \text{d}h \text{d}r ,

one for each point in the point pattern.

Note that the Euclidean procedure is implemented by the local K-functions of Adelfio et al. (2020), documented in KLISTAhat of the stpp package (Gabriel et al, 2013). The network case uses the local K-functions on networks (D'Angelo et al., 2021), documented in localSTLKinhom.

Value

A list object of class localdiag, containing

x

The stp object provided as input

listas

The LISTA functions, in a list object

ids

The ids of the points identified as outlying

x2

A vector with the individual contributions to the Chi-squared statistics, normalized

p

The percentile considered

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., 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

See Also

infl, plot.localdiag, print.localdiag, summary.localdiag, 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)

resmod1 <- localdiag(inh, mod1$l, p = .9)

Plot the coefficients of a fitted local spatio-temporal Poisson process or local LGCP model

Description

The function plots the local estimates of a fitted local spatio-temporal Poisson process or local LGCP model

Usage

localplot(x, par = TRUE)

Arguments

Author(s)

Nicoletta D'Angelo

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

locstppm, stlgcppm

Examples

# Local spatio-temporal Poisson process model

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, 
             par = c(0.005, 5))
inh_local <- locstppm(inh, formula = ~ x)

localplot(inh_local)

# Local LGCP
catsub <- stp(greececatalog$df[1:200, ])

lgcp_loc <- stlgcppm(catsub, formula = ~ x, first = "local")

localplot(lgcp_loc)

Summary plots of the fitted coefficient of a local spatio-temporal Poisson process or a local LGCP model

Description

The function breaks up the contribution of the local estimates to the fitted intensity, by plotting the overall intensity and the density kernel smoothing of some artificial intensities, obtained by imputing the quartiles of the local parameters' distributions.

Usage

localsummary(
  x,
  scaler = c("silverman", "IQR", "sd", "var"),
  do.points = TRUE,
  print.bw = FALSE,
  zap = 1e-05,
  par = TRUE
)

Arguments

Author(s)

Nicoletta D'Angelo and Giada Adelfio

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Davies, T.M. and Hazelton, M.L. (2010). Adaptive kernel estimation of spatial relative risk, Statistics in Medicine, 29(23) 2423-2437.

Terrell, G.R. (1990). The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 470-477.

See Also

locstppm, stlgcppm

Examples

# Local spatio-temporal Poisson process model

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, 
             par = c(0.005, 5))
inh_local <- locstppm(inh, formula = ~ x)

localsummary(inh_local)

# Local LGCP

catsub <- stp(greececatalog$df[1:200, ])

lgcp_loc <- stlgcppm(catsub, formula = ~ x, first = "local")

localsummary(lgcp_loc)

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

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)

Fit a local Poisson process model to a spatio-temporal point pattern

Description

This function fits a Poisson process model to an observed spatio-temporal point pattern stored in a stp object, that is, a Poisson model with a set of parameters \theta_i for each point i.

Usage

locstppm(
  X,
  formula,
  verbose = TRUE,
  mult = 4,
  seed = NULL,
  hs = c("global", "local"),
  npx0 = 10,
  npt0 = 10
)

Arguments

Details

We assume that the template model is a Poisson process, with a parametric intensity or rate function \lambda(\textbf{u}, t; \theta_i) with space and time locations \textbf{u} \in W, t \in T and parameters \theta_i \in \Theta.

Estimation is performed through the fitting of a glm using a localized version of the quadrature scheme by Berman and Turner (1992), firstly introduced in the purely spatial context by Baddeley (2017), and in the spatio-temporal framework by D'Angelo et al. (2023).

Value

An object of class locstppm. A list of

IntCoefs

The fitted global coefficients

IntCoefs_local

The fitted local coefficients

X

The stp object provided as input

nX

The number of points in X

I

Vector indicating which points are dummy or data

y_resp

The response variable of the model fitted to the quadrature scheme

formula

The formula provided as input

l

Fitted intensity through the global parameters

l_local

Fitted intensity through the local parameters

mod_global

The glm object of the model fitted to the quadrature scheme

newdata

The data used to fit the model, without the dummy points

time

Time elapsed to fit the model, in minutes

Author(s)

Nicoletta D'Angelo

References

Baddeley, A. (2017). Local composite likelihood for spatial point processes. Spatial Statistics, 22, 261-295.

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

stppm

Examples

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, 
             par = c(0.005, 5))
inh_local <- locstppm(inh, formula = ~ x)

Plot of the 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 plots of the inhomogeneous K-function weighted by the provided intensity to diagnose, its theoretical value, and their difference.

Usage

## S3 method for class 'globaldiag'
plot(x, samescale = TRUE, ...)

Arguments

Value

It plots three panels: the observed K-function, as returned by STLKinhom; the theoretical one; their difference. The function also prints the sum of squared differences between the observed and theoretical K-function on the console.

Author(s)

Nicoletta D'Angelo

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

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)

plot(g1)
plot(g2)

Display LISTA functions

Description

This function works on the objects of class lista, as returned by localSTLKinhom or localSTLginhom, plotting the specified LISTA functions.

Usage

## S3 method for class 'lista'
plot(x, id, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

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.

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

See Also

localSTLKinhom, localSTLginhom

Examples

set.seed(2)
df_net <- data.frame(x = runif(25, 0, 0.85), y = runif(25, 0, 0.85), t = runif(25))
stlp1 <- stp(df_net, L = chicagonet)
lambda <- rep(diff(range(stlp1$df$x)) * diff(range(stlp1$df$y))
 * diff(range(stlp1$df$t)) / spatstat.geom::volume(stlp1$L),
nrow(stlp1$df))

k <- localSTLKinhom(stlp1, lambda = lambda, normalize = TRUE)

plot(k, id = 1:9)

Plot of the local diagnostics' result on a spatio-temporal point process model

Description

This function plots the result of the local diagnostics performed with localdiag on either a stp or stlp object. It highlights the points of the analysed spatio-temporal point pattern X which are identified as outlying by the previously performed local diagnostics; the remaining points of X are also represented.

It also shows the underlying linear network, if the local diagnostics has been applied to point patterns occurring on the same linear network, that is, if localdiag has been applied to a stlp object.

Usage

## S3 method for class 'localdiag'
plot(x, marg = TRUE, col = "grey", col2 = "red", cols = "lightgrey", ...)

Arguments

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

See Also

infl, print.localdiag, summary.localdiag

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)

resmod1 <- localdiag(inh, mod1$l, p = .9)

plot(resmod1)
plot(resmod1, marg = FALSE)

Plot of the result of the local permutation test

Description

This function plots the result of the local permutation test performed with localtest on either a stp or stlp object. It highlights the points of the background pattern X, which exhibit local differences in the second-order structure with respect to Z, according to the previously performed test. The remaining points of X are also represented.

It also shows the underlying linear network, if the local test has been applied to point patterns occurring on the same linear network, that is, if localtest has been applied to a stlp object.

Usage

## S3 method for class 'localtest'
plot(x, col = "grey", cols = "lightgrey", col2 = "red", ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

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.

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

localtest, print.localtest, summary.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) 

plot(test)

Plot of the fitted intensity of a local spatio-temporal Poisson process model

Description

The function plots the local fitted intensity, displayed both in space and in space and time.

Usage

## S3 method for class 'locstppm'
plot(
  x,
  scaler = c("silverman", "IQR", "sd", "var"),
  do.points = TRUE,
  print.bw = FALSE,
  zap = 1e-05,
  par = TRUE,
  ...
)

Arguments

Author(s)

Nicoletta D'Angelo

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Davies, T.M. and Hazelton, M.L. (2010), Adaptive kernel estimation of spatial relative risk, Statistics in Medicine, 29(23) 2423-2437.

Terrell, G.R. (1990). The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 470-477.

See Also

locstppm, print.locstppm, summary.locstppm

Examples

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, 
             par = c(0.005, 5))
inh_local <- locstppm(inh, formula = ~ x)

plot(inh_local)

Plot of the fitted intensity of a separable spatio-temporal Poisson model

Description

The function plots the fitted intensity, displayed both in space and in space and time.

Usage

## S3 method for class 'sepstlppm'
plot(x, do.points = TRUE, par = TRUE, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)],
L = valencianet)

mod1 <- sepstlppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)
                  
plot(mod1)

Plot of the fitted intensity of a separable spatio-temporal Poisson model

Description

The function plots the fitted intensity, displayed both in space and in space and time.

Usage

## S3 method for class 'sepstppm'
plot(
  x,
  scaler = c("silverman", "IQR", "sd", "var"),
  do.points = TRUE,
  print.bw = FALSE,
  zap = 1e-05,
  par = TRUE,
  sig = NULL,
  ...
)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

crimesub <- stpm(valenciacrimes$df[1:100, ],
           names = colnames(valenciacrimes$df)[-c(1:3)])

mod1 <- sepstppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)
                  
plot(mod1)

Plot a stcov object

Description

This function plots the covariate stored in the stcov object given in input, in a three panel plot representing the 3Dplot of the coordinates, and the covariate values.

Usage

## S3 method for class 'stcov'
plot(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stcov

Examples

set.seed(2)
df <- data.frame(runif(100), runif(100), runif(100), rpois(100, 15))

cov <- stcov(df, interp = FALSE)

plot(cov)

Plot of the fitted intensity of a LGCP model

Description

The function plots the fitted intensity, displayed both in space and in space and time. In the case of local covariance parameters, the function returns the mean of the random intensity, displayed both in space and in space and time.

Usage

## S3 method for class 'stlgcppm'
plot(
  x,
  scaler = c("silverman", "IQR", "sd", "var"),
  do.points = TRUE,
  print.bw = FALSE,
  zap = 1e-05,
  par = TRUE,
  ...
)

Arguments

Author(s)

Nicoletta D'Angelo and Giada Adelfio

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Davies, T.M. and Hazelton, M.L. (2010), Adaptive kernel estimation of spatial relative risk, Statistics in Medicine, 29(23) 2423-2437.

Siino, M., Adelfio, G., and Mateu, J. (2018). Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes. Stochastic environmental research and risk assessment, 32(12), 3525-3539.

Terrell, G.R. (1990). The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 470-477.

See Also

stlgcppm, print.stlgcppm, summary.stlgcppm, localsummary, localplot

Examples

catsub <- stp(greececatalog$df[1:200, ])

lgcp_loc <- stlgcppm(catsub, formula = ~ x, first = "local")

plot(lgcp_loc)

Plot a stlp object

Description

This function plots the point pattern on a linear network stored in the stlp object given in input, in a three panel plot representing the plot3D of the coordinates, and the marginal spatial and temporal coordinates.

Usage

## S3 method for class 'stlp'
plot(x, tcum = TRUE, marg = TRUE, col = 1, cols = "grey", ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stp, summary.stlp, print.stlp

Examples

set.seed(2)
df_net <- data.frame(cbind(runif(100, 0, 0.85), runif(100, 0, 0.85), runif(100)))

stlp1 <- stp(df_net, L = chicagonet)

plot(stlp1)

Plot a stlpm object

Description

This function plots the covariate stored in the stcov object given in input, in a three panel plot representing the 3Dplot of the coordinates, and the mark values.

Usage

## S3 method for class 'stlpm'
plot(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stppm

Examples

set.seed(2)
df <- data.frame(x = runif(100, 0, 0.8), y = runif(100, 0, 0.8), t = runif(100), m = rpois(100, 15))

stlpm1 <- stpm(df, L = chicagonet)

plot(stlpm1)

Plot a stp object

Description

This function plots the point pattern stored in the stp object given in input, in a three panel plot representing the 3Dplot of the coordinates, and the marginal spatial and temporal coordinates.

Usage

## S3 method for class 'stp'
plot(x, tcum = TRUE, marg = TRUE, col = 1, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stp, print.stp, summary.stp

Examples

set.seed(2)
df <- data.frame(cbind(runif(100), runif(100), runif(100)))

stp1 <- stp(df)
#plot
plot(stp1)

#cumulative time occurrances
plot(stp1, tcum = FALSE)

#change color of points
plot(stp1, col = "blue")

#display only in space-time
plot(stp1, marg = FALSE)

#discrete times
set.seed(2)
stp2 <- stp(data.frame(cbind(runif(100), runif(100), round(runif(100) * 100))))
plot(stp2)

Plot a stpm object

Description

This function plots the marked point pattern stored in the stpm object given in input, in a three panel plot representing the 3Dplot of the coordinates, and the mark values.

Usage

## S3 method for class 'stpm'
plot(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stppm

Examples

df <- data.frame(cbind(runif(100), runif(100), runif(100), rpois(100, 15),
rpois(100, 30)))

stpm1 <- stpm(df)

plot(stpm1)

## Categorical marks

dfA <- data.frame(x = runif(100), y = runif(100), t = runif(100), 
                  m1 = rnorm(100), m2 = rep(c("C"), times = 100))
dfB <- data.frame(x = runif(50), y = runif(50), t = runif(50), 
                  m1 = rnorm(25), m2 = rep(c("D"), times = 50))

stpm2 <- stpm(rbind(dfA, dfB), names = c("continuous", "dichotomous"))

plot(stpm2)

Plot of the fitted intensity of a spatio-temporal Poisson process model

Description

The function plots the fitted intensity, displayed both in space and in space and time.

Usage

## S3 method for class 'stppm'
plot(
  x,
  scaler = c("silverman", "IQR", "sd", "var"),
  do.points = TRUE,
  print.bw = FALSE,
  zap = 1e-05,
  par = TRUE,
  ...
)

Arguments

Author(s)

Nicoletta D'Angelo and Giada Adelfio

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Davies, T.M. and Hazelton, M.L. (2010), Adaptive kernel estimation of spatial relative risk, Statistics in Medicine, 29(23) 2423-2437.

Terrell, G.R. (1990). The maximal smoothing principle in density estimation, Journal of the American Statistical Association, 85, 470-477.

See Also

stppm, print.stppm, summary.stppm

Examples

set.seed(2)
pin <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, par = c(2, 6),
nsim = 1, verbose = TRUE)
inh1 <- stppm(pin, formula = ~ x)

plot(inh1)

Print 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 sum of the squared differences between the estimated and the theoretical K-functions obtained through globaldiag.

Usage

## S3 method for class 'globaldiag'
print(x, ...)

Arguments

Value

It returns the sum of the squared differences between the estimated and the theoretical K-functions obtained through globaldiag

Author(s)

Nicoletta D'Angelo

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

globaldiag, plot.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)

g1
g2

Print a lista object

Description

It prints the main information on the local network summary statistics stored in a lista object.

Usage

## S3 method for class 'lista'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df_net <- data.frame(x = runif(25, 0, 0.85), y = runif(25, 0, 0.85), t = runif(25))
stlp1 <- stp(df_net, L = chicagonet)
lambda <- rep(diff(range(stlp1$df$x)) * diff(range(stlp1$df$y))
 * diff(range(stlp1$df$t)) / spatstat.geom::volume(stlp1$L),
nrow(stlp1$df))

k <- localSTLKinhom(stlp1, lambda = lambda, normalize = TRUE)

k

Print of the diagnostics' result on a spatio-temporal point process model

Description

It prints the main information on the result of the local diagnostics performed with localdiag on either a stp or stlp object: whether the local test was run on point patterns lying on a linear network or not; the number of points in the analysed spatio-temporal point pattern X; the number of points of X which are identified as outlying by the previously performed local diagnostics.

Usage

## S3 method for class 'localdiag'
print(x, ...)

Arguments

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

See Also

infl, plot.localdiag, summary.localdiag

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)

resmod1 <- localdiag(inh, mod1$l, p = .9)

resmod1

Print of the result of the permutation local test

Description

It prints the main information on the result of the local permutation test performed with localtest on either a stp or stlp object: whether the local test was run on point patterns lying on a linear network or not; the number of points in the background X and alternative Z patterns; the number of points in X which exhibit local differences in the second-order structure with respect to Z, according to the performed test.

Usage

## S3 method for class 'localtest'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

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.

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

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)

test

Print of a fitted local spatio-temporal Poisson process model

Description

The function prints the main information of the distribution of the parameters of a fitted local spatio-temporal Poisson process model.

Usage

## S3 method for class 'locstppm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

locstppm, summary.locstppm, plot.locstppm

Examples

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, 
             par = c(0.005, 5))
inh_local <- locstppm(inh, formula = ~ x)

inh_local

Print of a fitted separable spatio-temporal Poisson process model on a linear network

Description

The function prints the main information of the fitted model.

Usage

## S3 method for class 'sepstlppm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

sepstlppm

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)],
L = valencianet)

mod1 <- sepstlppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)
                  
mod1

Print of a fitted separable spatio-temporal Poisson process model

Description

The function prints the main information of the fitted model.

Usage

## S3 method for class 'sepstppm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

sepstppm

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)])

mod1 <- sepstppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)
mod1

Print a stcov object

Description

It prints the main information on the spatio-temporal covariate stored in the stcov object: the number of points; the enclosing spatial window; the temporal time period; information on the covariate values.

Usage

## S3 method for class 'stcov'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(runif(100), runif(100), runif(100), rpois(100, 15))

cov <- stcov(df, interp = FALSE)
cov

Print of a fitted LGCP model

Description

The function prints the main information on the fitted model. In this case of local parameters (both first- and second-order), the summary function contains information on their distributions.

Usage

## S3 method for class 'stlgcppm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo and Giada Adelfio

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Siino, M., Adelfio, G., and Mateu, J. (2018). Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes. Stochastic environmental research and risk assessment, 32(12), 3525-3539.

See Also

stlgcppm, print.stlgcppm, localsummary, plot.stlgcppm, localplot

Examples

catsub <- stp(greececatalog$df[1:200, ])

lgcp1 <- stlgcppm(catsub)

lgcp1

Print a stlp object

Description

It prints the main information on the spatio-temporal point pattern on a linear network stored in the stlp object: the number of points; vertices and lines of the linear network; the enclosing spatial window; the temporal time period.

Usage

## S3 method for class 'stlp'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stp, plot.stlp, summary.stlp

Examples

set.seed(2)
df_net <- data.frame(cbind(runif(100, 0, 0.85), runif(100, 0, 0.85), runif(100)))

stlp1 <- stp(df_net, L = chicagonet)
stlp1

Print a stlpm object

Description

It prints the main information on the spatio-temporal point pattern stored in the stlpm object: the number of points; the enclosing spatial window; the temporal time period; information on marks.

Usage

## S3 method for class 'stlpm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(x = runif(100, 0, 0.8), y = runif(100, 0, 0.8), t = runif(100), m = rpois(100, 15))

stlpm1 <- stpm(df, L = chicagonet)

stlpm1

Print a stp object

Description

It prints the main information on the spatio-temporal point pattern stored in the stp object: the number of points; the enclosing spatial window; the temporal time period.

Usage

## S3 method for class 'stp'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stp, summary.stp, plot.stp

Examples

set.seed(2)
df <- data.frame(cbind(runif(100), runif(100), runif(100)))

stp1 <- stp(df)
stp1

Print a stpm object

Description

It prints the main information on the spatio-temporal point pattern stored in the stpm object: the number of points; the enclosing spatial window; the temporal time period; information on marks.

Usage

## S3 method for class 'stpm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(cbind(runif(100), runif(100), runif(100), rpois(100, 15),
rpois(100, 30)))

stpm1 <- stpm(df)

summary(stpm1)

Print of a fitted spatio-temporal Poisson process model

Description

The function prints the main information of the fitted model.

Usage

## S3 method for class 'stppm'
print(x, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

stppm, print.stppm, plot.stppm

Examples

set.seed(2)
pin <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, par = c(2, 6))
inh1 <- stppm(pin, formula = ~ x)

inh1

Simulation of a spatio-temporal ETAS (Epidemic Type Aftershock Sequence) model on a linear network

Description

This function simulates a spatio-temporal ETAS (Epidemic Type Aftershock Sequence) process on a linear network as a stpm object.

It is firstly introduced and employed for simulation studies in D'Angelo et al. (2021).

It follows the generating scheme for simulating a pattern from an Epidemic Type Aftershocks-Sequences (ETAS) process (Ogata and Katsura 1988) with conditional intensity function (CIF) as in Adelfio and Chiodi (2020), adapted for the space location of events to be constrained on a linear network.

The simulation on the network is guaranteed by the homogeneous spatial Poisson processes being generated on the network.

Usage

rETASlp(
  pars = NULL,
  betacov = 0.39,
  m0 = 2.5,
  b = 1.0789,
  tmin = 0,
  t.lag = 200,
  covsim = FALSE,
  L,
  all.marks = FALSE
)

Arguments

Details

The CIF of an ETAS process as in Adelfio and Chiodi (2020) can be written as

\lambda_{\theta}(t,\textbf{u}|\mathcal{H}_t)=\mu f(\textbf{u})+\sum_{t_j<t} \frac{\kappa_0 \exp(\eta_j)}{(t-t_j+c)^p} \{ (\textbf{u}-\textbf{u}_j)^2+d \}^{-q} ,

where

\mathcal{H}_t is the past history of the process up to time t

\mu is the large-scale general intensity

f(\textbf{u}) is the spatial density

\eta_j=\boldsymbol{\beta}' \textbf{Z}_j is a linear predictor

\textbf{Z}_j the external known covariate vector, including the magnitude

\boldsymbol{\theta}= (\mu, \kappa_0, c, p, d, q, \boldsymbol{\beta}) are the parameters to be estimated

\kappa_0 is a normalising constant

c and p are characteristic parameters of the seismic activity of the given region,

and d and q are two parameters related to the spatial influence of the mainshock

In the usual ETAS model for seismic analyses, the only external covariate represents the magnitude, \boldsymbol{\beta}=\alpha, as \eta_j = \boldsymbol{\beta}' \textbf{Z}_j = \alpha (m_j-m_0), where m_j is the magnitude of the j^{th} event and m_0 the threshold magnitude, that is, the lower bound for which earthquakes with higher values of magnitude are surely recorded in the catalogue.

Value

A stlpm object

Author(s)

Nicoletta D'Angelo and Marcello Chiodi

References

Adelfio, G., and Chiodi, M. (2021). Including covariates in a space-time point process with application to seismicity. Statistical Methods & Applications, 30(3), 947-971.

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.

Ogata, Y., and Katsura, K. (1988). Likelihood analysis of spatial inhomogeneity for marked point patterns. Annals of the Institute of Statistical Mathematics, 40(1), 29-39.

Examples

set.seed(95)
X <- rETASlp(pars = c(0.1293688525, 0.003696, 0.013362, 1.2,0.424466,  1.164793),
     L = chicagonet)

Simulation of a spatio-temporal ETAS (Epidemic Type Aftershock Sequence) model

Description

This function simulates a spatio-temporal ETAS (Epidemic Type Aftershock Sequence) process as a stpm object.

It follows the generating scheme for simulating a pattern from an Epidemic Type Aftershocks-Sequences (ETAS) process (Ogata and Katsura 1988) with conditional intensity function (CIF) as in Adelfio and Chiodi (2020), adapted for the space location of events to be constrained.

See the 'Details' section.

Usage

rETASp(
  pars = NULL,
  betacov = 0.39,
  m0 = 2.5,
  b = 1.0789,
  tmin = 0,
  t.lag = 200,
  xmin = 0,
  xmax = 1,
  ymin = 0,
  ymax = 1,
  covsim = FALSE,
  all.marks = FALSE
)

Arguments

Details

The CIF of an ETAS process as in Adelfio and Chiodi (2020) can be written as

\lambda_{\theta}(t,\textbf{u}|\mathcal{H}_t)=\mu f(\textbf{u})+\sum_{t_j<t} \frac{\kappa_0 \exp(\eta_j)}{(t-t_j+c)^p} \{ (\textbf{u}-\textbf{u}_j)^2+d \}^{-q} ,

where

\mathcal{H}_t is the past history of the process up to time t

\mu is the large-scale general intensity

f(\textbf{u}) is the spatial density

\eta_j=\boldsymbol{\beta}' \textbf{Z}_j is a linear predictor

\textbf{Z}_j the external known covariate vector, including the magnitude

\boldsymbol{\theta}= (\mu, \kappa_0, c, p, d, q, \boldsymbol{\beta}) are the parameters to be estimated

\kappa_0 is a normalising constant

c and p are characteristic parameters of the seismic activity of the given region,

and d and q are two parameters related to the spatial influence of the mainshock

In the usual ETAS model for seismic analyses, the only external covariate represents the magnitude, \boldsymbol{\beta}=\alpha, as \eta_j = \boldsymbol{\beta}' \textbf{Z}_j = \alpha (m_j-m_0), where m_j is the magnitude of the j^{th} event and m_0 the threshold magnitude, that is, the lower bound for which earthquakes with higher values of magnitude are surely recorded in the catalogue.

Value

A stpm object

Author(s)

Nicoletta D'Angelo and Marcello Chiodi

References

Adelfio, G., and Chiodi, M. (2021). Including covariates in a space-time point process with application to seismicity. Statistical Methods & Applications, 30(3), 947-971.

Ogata, Y., and Katsura, K. (1988). Likelihood analysis of spatial inhomogeneity for marked point patterns. Annals of the Institute of Statistical Mathematics, 40(1), 29-39.

Examples

set.seed(95)
X <- rETASp(pars = c(0.1293688525, 0.003696, 0.013362, 1.2,0.424466,  1.164793),
         betacov = 0.5, 
         xmin = 600, xmax = 2200, ymin = 4000, ymax = 5300)

plot(X)

Simulate homogeneous and inhomogeneous spatio-temporal Poisson point patterns on linear networks

Description

This function creates a stlp object, simulating a spatio-temporal point pattern on a linear network following either an homogeneous or inhomogeneous intensity

Usage

rstlpp(
  lambda = 500,
  nsim = 1,
  verbose = FALSE,
  par = NULL,
  minX = 0,
  maxX = 1,
  minY = 0,
  maxY = 1,
  minT = 0,
  maxT = 1,
  L
)

Arguments

Value

A stp object

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
h1 <- rstlpp(lambda = 500, L = chicagonet)

set.seed(2)
inh <- rstlpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, par = c(4, 1.5),
        L = chicagonet)

Simulate homogeneous and inhomogeneous spatio-temporal Poisson point patterns

Description

This function creates a stp object, simulating a spatio-temporal point pattern following either an homogeneous or inhomogeneous intensity

Usage

rstpp(
  lambda = 500,
  nsim = 1,
  verbose = FALSE,
  par = NULL,
  minX = 0,
  maxX = 1,
  minY = 0,
  maxY = 1,
  minT = 0,
  maxT = 1
)

Arguments

Value

A stp object

Author(s)

Nicoletta D'Angelo

See Also

stppm

Examples

# homogeneous Poisson processes
set.seed(2)
h1 <- rstpp(lambda = 500)

set.seed(2)
h2 <- rstpp(lambda = 500, minX = 0,
             maxX = 2, minY = 3, maxY = 5, minT = 1, maxT = 9)

set.seed(2)
h3 <- rstpp(lambda = 900, nsim = 3, verbose = TRUE)

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

Fit a separable spatio-temporal Poisson process model on a linear network

Description

Fit a separable spatio-temporal Poisson process model on a linear network

Usage

sepstlppm(x, spaceformula, timeformula)

Arguments

Value

An object of class sepstlppm

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)],
L = valencianet)

mod1 <- sepstlppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)

Fit a separable spatio-temporal Poisson process model

Description

Fit a separable spatio-temporal Poisson process model

Usage

sepstppm(x, spaceformula, timeformula)

Arguments

Value

An object of class sepstppm

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)])

mod1 <- sepstppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)

Create stcov objects and interpolate spatio-temporal covariates on a regular grid

Description

This function interpolates the covariate values observed at some observed sites to a regular grid. The imput object should be either a matrix or a dataframe with four columns: x, y, t, and the covariate values, named as the covariate later called in the model formula (see stppm). The interpolation is performed through Inverse Distance Weighting (IDW). See the Details.

Usage

stcov(
  x,
  interp = TRUE,
  nx = NULL,
  mult = 1,
  p = 81,
  names = NULL,
  verbose = FALSE
)

Arguments

Details

The function builds a regular grid with equispaced values along the three coordinates and interpolates the covariate values at the new locations. The interpolation at a point location x_k is performed through the inverse-distance weighting smoothing procedure of the covariate values Z(x_j) at their sampling locations j=1, \ldots, J. In such a case, the smoothed value at location x_k is

Z(x_k) = \frac{\sum_j w_j Z(x_j)}{\sum_j w_j},

where the weight w_j is the j-th element of the inverse pth powers of distance,

\textbf{w}=\{w_j\}_{j=1}^J=\{\frac{1}{d(x_k-x_j)^p}\}_{j=1}^J,

with

d(x_k-x_j) = ||x_k-x_j||

the Euclidean distance from x_k to x_j.

Value

A stpm object, to be imputed as list object in stppm.

Author(s)

Nicoletta D'Angelo

See Also

stppm

Examples

set.seed(2)
df <- data.frame(runif(100), runif(100), runif(100), rpois(100, 15))

cov <- stcov(df, interp = FALSE)

Fit a log-Gaussian Cox process model to a spatio-temporal point pattern

Description

This function estimates a log-Gaussian Cox process (LGCP), following the **joint minimum contrast** procedure introduced in Siino et al. (2018) .

Three covariances are available: separable exponential, Gneiting, and De Iaco-Cesare.

If the first and second arguments are set to local, a local log-Gaussian Cox process is fitted by means of the ** locally weighted minimum contrast** procedure proposed in D'Angelo et al. (2023).

Usage

stlgcppm(
  X,
  formula = ~1,
  verbose = TRUE,
  seed = NULL,
  cov = c("separable", "gneiting", "iaco-cesare"),
  first = c("global", "local"),
  second = c("global", "local"),
  mult = 4,
  hs = c("global", "local"),
  npx0 = 10,
  npt0 = 10,
  itnmax = 100,
  min_vals = NULL,
  max_vals = NULL
)

Arguments

Details

Following the inhomogeneous specification in Diggle et al. (2013), we consider LGCPs with intensity

\Lambda(\textbf{u},t)=\lambda(\textbf{u},t)\exp(S(\textbf{u},t)).

Value

A list of the class stlgcppm, containing

IntCoefs

The fitted coefficients of the first-order intensity function

CovCoefs

The fitted coefficients of the second-order intensity function

X

The stp object provided as input

formula

The formula provided as input

cov

A string with the chosen covariance type

l

Fitted first-order intensity

mu

Mean function of the random intensity

mod_global

The glm object of the model fitted to the quadrature scheme for the first-order intensity parameters estimation

newdata

The data used to fit the model, without the dummy points

time

Time elapsed to fit the model, in minutes

Author(s)

Nicoletta D'Angelo, Giada Adelfio, and Marianna Siino

References

Baddeley, A. (2017). Local composite likelihood for spatial point processes. Spatial Statistics, 22, 261-295.

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Diggle, P. J., Moraga, P., Rowlingson, B., and Taylor, B. M. (2013). Spatial and spatio-temporal log-gaussian cox processes: extending the geostatistical paradigm. Statistical Science, 28(4):542–563.

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., Adelfio, G., and Mateu, J. (2018). Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes. Stochastic environmental research and risk assessment, 32(12), 3525-3539.

See Also

print.stlgcppm, summary.stlgcppm, localsummary, plot.stlgcppm, localplot

Examples

catsub <- stp(greececatalog$df[1:200, ])

lgcp1 <- stlgcppm(catsub)

Create stp and stlp objects for point patterns storage

Description

This function creates a stp object as a dataframe with three columns: x, y, and t. If also the linear network L, of class linnet, is provided, a stlp object is created instead.

Usage

stp(df, L)

Arguments

Value

An stp or stlpp object, depending on whether or not an object of class linnet is provided for the L argument.

Author(s)

Nicoletta D'Angelo

See Also

summary.stp, print.stp, plot.stp

stppm, print.stp, summary.stp, plot.stp, print.stlp, summary.stlp, plot.stlp

Examples

set.seed(2)
df <- data.frame(runif(100), runif(100), runif(100))

stp1 <- stp(df)

set.seed(2)                       
df_net <- data.frame(runif(100, 0, 0.85), runif(100, 0, 0.85), runif(100))

stlp1 <- stp(df_net, L = chicagonet)

Create stpm and stlpm objects for marked point patterns storage

Description

This function creates a stpm object as a dataframe with 3 + m columns: x, y, t, and m columns to store different marks. If also the linear network L, of class linnet, is provided, a stlp object is created instead.

Usage

stpm(df, names = NULL, L)

Arguments

Value

An stpm or stlppm object, depending on whether or not an object of class linnet is provided for the L argument.

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(cbind(runif(100), runif(100), runif(100), rpois(100, 15),
rpois(100, 30)))

stpm1 <- stpm(df)

## Categorical marks

set.seed(2)
dfA <- data.frame(x = runif(100), y = runif(100), t = runif(100), 
                  m1 = rnorm(100), m2 = rep(c("C"), times = 100))
dfB <- data.frame(x = runif(50), y = runif(50), t = runif(50), 
                  m1 = rnorm(25), m2 = rep(c("D"), times = 50))

stpm2 <- stpm(rbind(dfA, dfB), names = c("continuous", "dichotomous"))

## Linear network

set.seed(2)
dfL <- data.frame(cbind(runif(100, 0, 0.85), runif(100, 0, 0.85), runif(100), 
                       rpois(100, 15)))

stlpm1 <- stpm(dfL, L = chicagonet)

Fit a Poisson process model to a spatio-temporal point pattern

Description

This function fits a Poisson process model to an observed spatio-temporal point pattern stored in a stp object.

Usage

stppm(
  X,
  formula,
  formula_mark = NULL,
  covs = NULL,
  marked = FALSE,
  spatial.cov = FALSE,
  verbose = FALSE,
  mult = 4,
  interp = TRUE,
  parallel = FALSE,
  sites = 1,
  seed = NULL,
  ncube = NULL,
  grid = FALSE,
  ncores = 2,
  lsr = FALSE
)

Arguments

Details

We assume that the template model is a Poisson process, with a parametric intensity or rate function \lambda(\textbf{u}, t; \theta) with space and time locations \textbf{u} \in W, t \in T and parameters \theta \in \Theta.

Estimation is performed through the fitting of a glm using a spatio-temporal version of the quadrature scheme by Berman and Turner (1992).

Value

An object of class stppm. A list of

IntCoefs

The fitted coefficients

X

The stp object provided as input

nX

The number of points in X

I

Vector indicating which points are dummy or data

y_resp

The response variable of the model fitted to the quadrature scheme

formula

The formula provided as input

l

Fitted intensity

mod_global

The glm object of the model fitted to the quadrature scheme

newdata

The data used to fit the model, without the dummy points

time

Time elapsed to fit the model, in minutes

Author(s)

Nicoletta D'Angelo and Marco Tarantino

References

Baddeley, A. J., Møller, J., and Waagepetersen, R. (2000). Non-and semi-parametric estimation of interaction in inhomogeneous point patterns. Statistica Neerlandica, 54(3):329–350

Berman, M. and Turner, T. R. (1992). Approximating point process likelihoods with glim. Journal of the Royal Statistical Society: Series C (Applied Statistics), 41(1):31–38

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

plot.stppm, print.stppm, summary.stppm

locstppm

Examples

set.seed(2)
ph <- rstpp(lambda = 200)
hom1 <- stppm(ph, formula = ~ 1)

## Inhomogeneous
set.seed(2)
pin <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, par = c(2, 6))
inh1 <- stppm(pin, formula = ~ x)

## Inhomogeneous depending on external covariates

set.seed(2)
df1 <- data.frame(runif(100), runif(100), runif(100), rpois(100, 15))
df2 <- data.frame(runif(100), runif(100), runif(100), rpois(100, 15))

obj1 <- stcov(df1, names = "cov1")
obj2 <- stcov(df2, names = "cov2")

covariates <- list(cov1 = obj1, cov2 = obj2)

inh2 <- stppm(pin, formula = ~ x + cov2, covs = covariates, spatial.cov = TRUE)

## Inhomogeneous semiparametric

inh3 <- stppm(pin, formula = ~ s(x, k = 30))

## Multitype

set.seed(2)
dfA <- data.frame(x = runif(100), y = runif(100), t = runif(100), 
                  m1 = rep(c("A"), times = 100))
dfB <- data.frame(x = runif(50), y = runif(50), t = runif(50), 
                  m1 = rep(c("B"), each = 50))

stpm1 <- stpm(rbind(dfA, dfB))

inh4 <- stppm(stpm1, formula = ~ x + s(m1, bs = "re"), marked = TRUE)

Summarizes 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 sum of the squared differences between the estimated and the theoretical K-functions obtained through globaldiag.

Usage

## S3 method for class 'globaldiag'
summary(object, ...)

Arguments

Value

It returns the sum of the squared differences between the estimated and the theoretical K-functions obtained through globaldiag

Author(s)

Nicoletta D'Angelo

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

globaldiag, plot.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)

summary(g1)
summary(g2)

Summary a lista object

Description

It prints the main information on the local network summary statistics stored in a lista object.

Usage

## S3 method for class 'lista'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df_net <- data.frame(x = runif(25, 0, 0.85), y = runif(25, 0, 0.85), t = runif(25))
stlp1 <- stp(df_net, L = chicagonet)
lambda <- rep(diff(range(stlp1$df$x)) * diff(range(stlp1$df$y))
 * diff(range(stlp1$df$t)) / spatstat.geom::volume(stlp1$L),
nrow(stlp1$df))

k <- localSTLKinhom(stlp1, lambda = lambda, normalize = TRUE)

summary(k)

Summary of the diagnostics performed on a spatio-temporal point process model

Description

It summarises the main information on the result of the local diagnostics performed with localdiag on either a stp or stlp object: whether the local test was run on point patterns lying on a linear network or not; the number of points in the analysed spatio-temporal point pattern X; the number of points of X which are identified as outlying by the previously performed local diagnostics.

Usage

## S3 method for class 'localdiag'
summary(object, ...)

Arguments

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

See Also

infl, plot.localdiag, print.localdiag

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)

resmod1 <- localdiag(inh, mod1$l, p = .9)

summary(resmod1)

Summary of the result of the permutation local test

Description

It summarises the main information on the result of the local permutation test performed with localtest on either a stp or stlp object: whether the local test was run on point patterns lying on a linear network or not; the number of points in the background X and alternative Z patterns; the number of points in X which exhibit local differences in the second-order structure with respect to Z, according to the performed test.

Usage

## S3 method for class 'localtest'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

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.

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

localtest, print.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)

summary(test)

Summary of a fitted local spatio-temporal Poisson process model

Description

The function summarises the main information on the distribution of the parameters of a fitted local spatio-temporal Poisson process model.

Usage

## S3 method for class 'locstppm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

locstppm, print.locstppm, plot.locstppm

Examples

set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, 
             par = c(0.005, 5))
inh_local <- locstppm(inh, formula = ~ x)

summary(inh_local)

Summary of a fitted fitted separable spatio-temporal Poisson process model on a linear network

Description

The function summarises the main information of the fitted model.

Usage

## S3 method for class 'sepstlppm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

sepstlppm

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)],
L = valencianet)

mod1 <- sepstlppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)
                  
summary(mod1)

Summary of a fitted separable spatio-temporal Poisson process model

Description

The function summarises the main information of the fitted model.

Usage

## S3 method for class 'sepstppm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

sepstlppm

Examples

crimesub <- stpm(valenciacrimes$df[101:200, ],
           names = colnames(valenciacrimes$df)[-c(1:3)])

mod1 <- sepstppm(crimesub, spaceformula = ~x ,
                  timeformula = ~ day)
                  
summary(mod1)

Summary of a stcov object

Description

It prints the summary statistics of the spatio-temporal coordinates and the covariates values of the spatio-temporal covariate stored in the stcov object.

Usage

## S3 method for class 'stcov'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(runif(100), runif(100), runif(100), rpois(100, 15))

cov <- stcov(df, interp = FALSE)
summary(cov)

Summary of a fitted LGCP model

Description

The function Summarises the main information on the fitted model. provided. In this case of local parameters (both first- and second-order), the summary function contains information on their distributions.

Usage

## S3 method for class 'stlgcppm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo and Giada Adelfio

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

Siino, M., Adelfio, G., and Mateu, J. (2018). Joint second-order parameter estimation for spatio-temporal log-Gaussian Cox processes. Stochastic environmental research and risk assessment, 32(12), 3525-3539.

See Also

stlgcppm, print.stlgcppm, localsummary, plot.stlgcppm, localplot

Examples

catsub <- stp(greececatalog$df[1:200, ])

lgcp1 <- stlgcppm(catsub)

summary(lgcp1)

Summary of a stlp object

Description

It prints the main information on the spatio-temporal point pattern on a linear network stored in the stlp object: the number of points; vertices and lines of the linear network; the enclosing spatial window; the temporal time period.

Usage

## S3 method for class 'stlp'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stp, plot.stlp, print.stlp

Examples

set.seed(2)                       
df_net <- data.frame(cbind(runif(100, 0, 0.85), runif(100, 0, 0.85), runif(100)))

stlp1 <- stp(df_net, L = chicagonet)
summary(stlp1)

Summary of a stlpm object

Description

It prints the summary statistics of the spatio-temporal coordinates and the marks of the spatio-temporal point pattern stored in the stlpm object.

Usage

## S3 method for class 'stlpm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(x = runif(100, 0, 0.8), y = runif(100, 0, 0.8),
 t = runif(100), m = rpois(100, 15))

stlpm1 <- stpm(df, L = chicagonet)

summary(stlpm1)

Summary of a stp object

Description

It prints the summary statistics of the spatial and temporal coordinates of the spatio-temporal point pattern stored in the stp object.

Usage

## S3 method for class 'stp'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

See Also

stp, print.stp, plot.stp

Examples

set.seed(2)
df <- data.frame(cbind(runif(100), runif(100), runif(100)))

stp1 <- stp(df)
summary(stp1)

Summary of a stpm object

Description

It prints the summary statistics of the spatio-temporal coordinates and the marks of the spatio-temporal point pattern stored in the stpm object.

Usage

## S3 method for class 'stpm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

Examples

set.seed(2)
df <- data.frame(cbind(runif(100), runif(100), runif(100), rpois(100, 15),
rpois(100, 30)))

stpm1 <- stpm(df)

summary(stpm1)

## Categorical marks

set.seed(2)
dfA <- data.frame(x = runif(100), y = runif(100), t = runif(100), 
                  m1 = rnorm(100), m2 = rep(c("C"), times = 100))
dfB <- data.frame(x = runif(50), y = runif(50), t = runif(50), 
                  m1 = rnorm(25), m2 = rep(c("D"), times = 50))

stpm2 <- stpm(rbind(dfA, dfB), names = c("continuous", "dichotomous"))

summary(stpm2)

Summary of a fitted spatio-temporal Poisson process model

Description

The function summarises the main information of the fitted model.

Usage

## S3 method for class 'stppm'
summary(object, ...)

Arguments

Author(s)

Nicoletta D'Angelo

References

D'Angelo, N., Adelfio, G., and Mateu, J. (2023). Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes. Computational Statistics & Data Analysis, 180, 107679.

See Also

stppm, print.stppm, plot.stppm

Examples

set.seed(2)
pin <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)}, par = c(2, 6))
inh1 <- stppm(pin, formula = ~ x)

summary(inh1)

Crimes in Valencia in 2019

Description

A dataset in stpm format containing the 10929 crimes occurred in Valencia, Spain, in 2019.

Usage

data(valenciacrimes)

Format

A stpm object

Details

The 15 available marks are the following:

• month.

• week.

• day.

• week_day.

• atm_dist.

• bank_dist.

• bar_dist.

• cafe_dist.

• industrial_dist.

• market_dist.

• nightclub_dist.

• police_dist.

• pub_dist.

• restaurant_dist.

• taxi_dist.

Author(s)

Nicoletta D'Angelo

Examples

data(valenciacrimes)

Roads of Valencia, Spain

Description

A linear network of class linnet of the roads of Valencia, Spain

Usage

data(valencianet)

Format

A linear network of class linnet

Author(s)

Nicoletta D'Angelo

Examples

data(valencianet)