| Type: | Package |
| Version: | 0.4.0 |
| Title: | Spatio-Temporal Analysis of Point Patterns on Linear Networks |
| Maintainer: | Mehdi Moradi <m2.moradi@yahoo.com> |
| Description: | Statistical analysis of spatio-temporal point processes on linear networks. This packages provides tools to visualise and analyse spatio-temporal point patterns on linear networks using first- and second-order summary statistics. |
| Depends: | R (≥ 3.3.0), spatstat (≥ 2.0-0) |
| Imports: | spatstat.univar, spatstat.geom, spatstat.random, spatstat.explore, spatstat.linnet, stats, graphics |
| Suggests: | plot3D, lattice |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2024-05-27 08:19:06 UTC; memo0042 |
| Author: | Mehdi Moradi 
[aut, cre],
Ottmar Cronie [ctb],
Jorge Mateu [ctb] |
| Repository: | CRAN |
| Date/Publication: | 2024-05-27 12:10:22 UTC |
Eastbourne traffic accident data
Description
This dataset represents the spatio-temporal locations of traffic accidents in the down-town of Eastbourne (UK) in the period of 2005-2010. The network was provided by “OS OpenData" at www.ordnancesurvey.co.uk and is usable under the terms of the OS OpenData license. The traffic locations were collected by the UK Department for Transport at www.data.gov.uk and obtained through kaggle at www.kaggle.com.
The dataset Eastbourne is an object of class stlpp.
Usage
data(Eastbourne)
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
Source
Usability: The network of Eastbourne was provided by OS OpenData and contains OS data © Crown copyright and database right (2018). The traffic accident locations in Eastbourne were collected by the UK Department for Transport and were provided by kaggle.
This data is a part of enitre data which is selected and converted to this format by Mehdi Moradi.
References
Moradi, M., & 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
Examples
data(Eastbourne)
plot(Eastbourne)
Medellin traffic accident data
Description
This dataset represents the spatio-temporal locations of traffic accidents in an area near the pontifical bolivarian university in Medellin (Colombia) during 2016. The entire data were published in the OpenData portal of Medellin Town Hall at https://www.medellin.gov.co/geomedellin/index.hyg.
The dataset Medellin is an object of class stlpp.
Usage
data(Medellin)
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
Source
This data is a part of enitre data which is selected and converted to this format by Mehdi Moradi.
References
Moradi, M., & 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
Examples
data(Medellin)
plot(Medellin)
K-function for spatio-temporal point processes on linear networks
Description
This function computes the K-function for spatio-temporal point patterns on linear networks.
Usage
STLK(X,r=NULL,t=NULL,nxy=10)
Arguments
X |
a spatio-temporal point pattern of class |
r |
values of argument r where pair correlation function will be evaluated. optional |
t |
values of argument t where pair correlation function will be evaluated. optional |
nxy |
pixel array dimensions. optional |
Details
This function calculates the K-function for a homogeneous spatio-temporal point patterns on a linear network.
Value
An object of class sumstlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
Kest, STLg
Examples
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
k <- STLK(X)
plot(k)
Inhomogeneous K-function for spatio-temporal point processes on linear networks
Description
This function computes the inhomogeneous K-function for spatio-temporal point patterns on linear networks.
Usage
STLKinhom(X,lambda=lambda,normalize=FALSE,r=NULL,t=NULL,nxy=10)
Arguments
X |
a spatio-temporal point pattern of class |
lambda |
values of estimated intensity at data points |
normalize |
normalization factor to be considered |
r |
values of argument r where pair correlation function will be evaluated. optional |
t |
values of argument t where pair correlation function will be evaluated. optional |
nxy |
pixel array dimensions. optional |
Details
This function calculates the inhomogeneous K-function for a spatio-temporal point patterns on a linear network.
Value
An object of class sumstlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
Examples
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
lambda <- density(X,at="points")
k <- STLKinhom(X,lambda=lambda,normalize=TRUE)
plot(k)
Pair correlation function for spatio-temporal point processes on linear networks
Description
This function computes the pair correlation function for spatio-temporal point patterns on linear networks.
Usage
STLg(X,r=NULL,t=NULL,nxy=10)
Arguments
X |
a spatio-temporal point pattern of class |
r |
values of argument r where pair correlation function will be evaluated. optional |
t |
values of argument t where pair correlation function will be evaluated. optional |
nxy |
pixel array dimensions. optional |
Details
This function calculates the pair correlation function for a homogeneous spatio-temporal point patterns on a linear network.
Value
An object of class sumstlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
pcf, STLK
Examples
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
g <- STLg(X)
plot(g)
Inhomogeneous pair correlation function for spatio-temporal point processes on linear networks
Description
This function computes the inhomogeneous pair correlation function for spatio-temporal point patterns on linear networks.
Usage
STLginhom(X,lambda,normalize=FALSE,r=NULL,t=NULL,nxy=10)
Arguments
X |
a spatio-temporal point pattern of class |
lambda |
values of estimated intensity at data points |
normalize |
normalization factor to be considered |
r |
values of argument r where pair correlation function will be evaluated. optional |
t |
values of argument t where pair correlation function will be evaluated. optional |
nxy |
pixel array dimensions. optional |
Details
This function calculates the inhomogeneous pair correlation function for a spatio-temporal point patterns on a linear network.
Value
An object of class sumstlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
Examples
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
d <- density(X,at="points")
g <- STLginhom(X,lambda=d,normalize=TRUE)
plot(g)
Methods for spatio-temporal point patterns on a linear network
Description
This function projects an object of class stlpp into a linear network.
Usage
## S3 method for class 'stlpp'
as.lpp(x,...)
Arguments
x |
an object of class |
... |
arguments passed to |
Details
This function projects the spatio-temporal point pattern x on the linear network L into L, giving its corresponding spatial point pattern.
Value
An object of class lpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
See Also
as.stlpp, lpp, as.lpp
Examples
data(easynet)
x <- runifpointOnLines(40, easynet)
t1 <- sample(1:10,40,replace=TRUE)
Y <- as.stlpp(x,t=t1,L=easynet)
as.lpp.stlpp(Y)
Convert data to a spatio-temporal point pattern on a linear network
Description
This function converts data to a spatio-temporal point pattern on a linear network.
Usage
as.stlpp(x,y,t,L)
Arguments
x, y, t |
vectors of Cartesian coordinates and time occurrence. Alternatively, x can be of classes |
L |
linear network (object of class |
Details
This function converts data to an object of class stlpp. Data can be of formats:
x is of class class
data.framewith three columns. Then columns are considered as Cartesian coordinates (i.e. x,y,t) and they will be converted to a spatio-temporal point pattern on the linear network L.x is a planar point pattern (class
ppp). Then x will be converted to a spatio-temporal point pattern on the linear network L and with coresponding time vector t.x is a linear point pattern (class
lpp). Then x will be converted to a spatio-temporal point pattern on the linear network L and with coresponding time vector t.x,y,t are vectors of same length where x,y are living on the corresponding network L.
Value
A spatio-temporal point pattern on a linear network. An object of class stlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
See Also
Examples
data(easynet)
x <- runifpointOnLines(40, easynet)
t1 <- sample(1:10,40,replace=TRUE)
Y <- as.stlpp(x,t=t1,L=easynet)
Z <- as.lpp.stlpp(Y)
t2 <- sample(1:10,40,replace=TRUE)
W <- as.stlpp(Z,t=t2)
Convert data to a one-dimensional point pattern
Description
This function converts an object of class stlpp to class tpp.
Usage
as.tpp.stlpp(X)
Arguments
X |
an object of class |
Details
This function projects the spatio-temporal point pattern X into its corresponding time domain T.
Value
An object of class tpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
See Also
as.stlpp, lpp, as.lpp
Examples
X <- rpoistlpp(10,1,2,easynet)
as.tpp.stlpp(X)
Kernel estimation of intensity of spatio-temporal point patterns on a linear network
Description
Kernel density estimation of a spatio-temporal point pattern on a linear network.
Usage
## S3 method for class 'stlpp'
density(x,lbw,tbw,at=c("points","pixels"),dimt=512,...)
Arguments
x |
an object of class |
lbw |
network smoothing bandwidth |
tbw |
time smoothing bandwidth |
at |
string specifying whether to compute the intensity values at a grid of pixel locations and times (at="pixels") or only at the points of x (at="points"). default is to estimate the intensity at pixels |
dimt |
the number of equally spaced points at which the temporal density is to be estimated. see density |
... |
arguments passed to |
Details
Kernel smoothing is applied to the spatio-temporal point pattern x using methods in Moradi et al (2019). The function computes estimated intensities assuming first-order separability. Estimated intensity values of the marginal spatial point pattern on the linear network will be obtained using the fast kernel smoothing technique of Rakshit et al. (2019) and function densityQuick.lpp, whereas the estimated intensity values of the marginal temporal point pattern will be estimated using the function density.
If lbw and tbw are not given, then they will be selected using bw.nrd0 and bw.scott.iso respectively.
Value
If at="points": a vector of intensity values at the data points of x.
If at="pixels": a list of images on linear network. Each image represents an estimated spatio-temporal intensity at a fixed time.
Check the attributes for more accommodated outputs.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
density, density.lpp, bw.nrd0, bw.scott.iso
Examples
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
density(X)
Kernel estimation of intensity of one-dimensional point patterns
Description
Kernel estimation of intensity of one-dimensional point patterns.
Usage
## S3 method for class 'tpp'
density(x,tbw,at=c("points","pixels"),...)
Arguments
x |
an object of class |
tbw |
time smoothing bandwidth |
at |
string specifying whether to compute the intensity values at a grid of pixel locations (at="pixels") or only at the points of x (at="points"). default is to estimate the intensity at pixels |
... |
arguments passed to density |
Details
A vector of intensity values.
Value
If at="points": a vector of intensity values at the data points of x.
If at="pixels": a vector of intensity values over a grid.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com> and Ottmar Cronie
References
Mateu, J., Moradi, M., & Cronie, O. (2019). Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation. Spatial Statistics, 100400.
See Also
Examples
X <- tpp(sample(c(1:24),200,replace = TRUE))
plot(density(X))
Intensity estimate of spatio-temporal point pattern using Voronoi-Dirichlet tessellation
Description
This function performs adaptive intensity estimation for spatio-temporal point patterns on linear networks using Voronoi-Dirichlet tessellation.
Usage
## S3 method for class 'stlpp'
densityVoronoi(X, f = 1, nrep = 1, separable=FALSE, at=c("points","pixels"), dimt=128,...)
Arguments
X |
an object of class |
f |
fraction (between 0 and 1 inclusive) of the data points that will be used to build a tessellation for the intensity estimate |
nrep |
number of independent repetitions of the randomised procedure |
separable |
logical. If FALSE, it then calculates a pseudo-separable estimate |
at |
string specifying whether to compute the intensity values at a grid of pixel locations and time (at="pixels") or only at the points of x (at="points"). default is to estimate the intensity at pixels |
dimt |
the number of equally spaced points at which the temporal density is to be estimated. see density |
... |
arguments passed to |
Details
This function computes intensity estimates for spatio-temporal point patterns on linear networks using Voronoi-Dirichlet tessellation. Both first-order separability and pseudo-separability assumptions are accommodated in the function.
If separable=TRUE, the estimated intensities will be a product of the estimated intensities on the network and those on time. Estimated intensity of the spatial component will be obtained using densityVoronoi.lpp, whereas estimated intensities of the temporal component will be obtained via densityVoronoi.tpp. If f=1, the function calculates the estimations based on the original Voronoi intensity estimator.
If separable=FALSE, the estimated intensities will be calculated based on a sub-sampling technique explained in Mateu et al. (2019). nrep sub-samples will be obtained from X based on a given retention probability f, the function densityVoronoi.stlpp, considering separable=TRUE and f=1, will be applied to each obtained sub-sample, and finally, the estimated intensities will be the sum of all obtained estimated intensities from all sub-samples divided by the (f * nrep).
Value
If at="points": a vector of intensity values at the data points of X.
If at="pixels": a list of images on a linear network. Each image represents an estimated spatio-temporal intensity at a fixed time.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com> and Ottmar Cronie
References
Mateu, J., Moradi, M., & Cronie, O. (2019). Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation. Spatial Statistics, 100400.
See Also
densityVoronoi.lpp, density.stlpp
Examples
X <- rpoistlpp(.2,a=0,b=5,L=easynet)
densityVoronoi(X)
Intensity estimate of temporal point patterns using Voronoi-Dirichlet tessellation
Description
This function performs adaptive intensity estimation for temporal point patterns using Voronoi-Dirichlet tessellation.
Usage
## S3 method for class 'tpp'
densityVoronoi(X, f = 1, nrep = 1, at=c("points","pixels"), dimt=128,...)
Arguments
X |
an object of class |
f |
fraction (between 0 and 1 inclusive) of the data points that will be used to build a tessellation for the intensity estimate |
nrep |
number of independent repetitions of the randomised procedure |
at |
string specifying whether to compute the intensity values at a grid of pixel locations and time (at="pixels") or only at the points of x (at="points"). default is to estimate the intensity at pixels |
dimt |
the number of equally spaced points at which the temporal density is to be estimated. see density |
... |
arguments passed to |
Details
This function computes intensity estimates for temporal point patterns using Voronoi-Dirichlet tessellation.
IF f<1, then nrep independent sub-samples of X are obtained using the function rthin.stlpp. Then for each of the obtained sub-samples, we calculate the Voronoi estimate. The final estimation is the sum of all obtained estimated intensities divided by (f*nrep).
Value
If at="points": a vector of intensity values at the data points of X.
If at="pixels": a vector of intensity values over a grid.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com> and Ottmar Cronie
References
Mateu, J., Moradi, M., & Cronie, O. (2019). Spatio-temporal point patterns on linear networks: Pseudo-separable intensity estimation. Spatial Statistics, 100400.
See Also
densityVoronoi.lpp, density.stlpp
Examples
X <- rpoistlpp(0.2,a=0,b=5,L=easynet)
Y <- as.tpp.stlpp(X)
densityVoronoi(Y)
A simple linear network
Description
A simple and not real network.
Usage
data(easynet)
Source
Created by Mehdi Moradi
Methods for space-time point patterns on a linear network
Description
Methods for space-time point patterns on a linear network.
Usage
## S3 method for class 'stlpp'
plot(x,xlab = xlab,...)
## S3 method for class 'stlppint'
plot(x,style=style,xlab=xlab,xlim=xlim,ylim=ylim,bar=TRUE,...)
## S3 method for class 'sumstlpp'
plot(x,style=c("level","contour","perspective"), theta = 35, phi = 10,
facets = FALSE, ticktype = "detailed", resfac = 5,xlab="r = distance",ylab="t = time",...)
## S3 method for class 'stlpp'
print(x,...)
## S3 method for class 'stlppint'
print(x,...)
## S3 method for class 'sumstlpp'
print(x,...)
## S3 method for class 'stlpp'
x[i]
## S3 method for class 'stlppint'
x[i]
## S3 method for class 'stlppint'
as.linim(X,...)
## S3 method for class 'stlppint'
as.tppint(x)
## S3 method for class 'sumstlpp'
as.data.frame(x,...)
Arguments
x, X |
an object of classes |
style |
style of plot |
theta, phi |
see persp3D |
facets, ticktype |
see persp3D |
resfac |
see persp3D |
xlab, ylab |
the x,y label of the plot |
xlim |
giving the x limits for the plot |
ylim |
giving the y limits for the plot |
bar |
if TRUE, bar plot of rounded time occurances will be added to the density plot |
i |
numeric, logical, or an object of class |
... |
either ignore for |
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
Methods for one-dimensional point patterns
Description
Methods for one-dimensional point patterns.
Usage
## S3 method for class 'tpp'
plot(x,xlab="time",ylab="",main = "cumulative number",...)
## S3 method for class 'tppint'
plot(x,xlab=xlab,xlim=xlim,line=2.5,main="NULL",...)
## S3 method for class 'tpp'
print(x,...)
## S3 method for class 'tppint'
print(x,...)
## S3 method for class 'tpp'
x[i]
## S3 method for class 'tppint'
x[i]
Arguments
x |
an object of class tpp or tppint. |
xlab, ylab |
the x,y label of the plot. |
main |
overall title for the plot. |
xlim |
giving the x limits for the plot. |
line |
specifying a value for line overrides the default placement of y label, and places it this many lines outwards from the plot edge. |
i |
numeric, logical, or an object of class |
... |
graphics parameters passed to plot/print function. |
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
Examples
X <- tpp(sample(c(1:24),200,replace = TRUE))
plot(X)
plot(density(X))
Simulating spatio-temporal Poisson point processes on a linear network
Description
This function simulates realisations of a spatio-temporal Poisson point process on a linear network.
Usage
rpoistlpp(lambda,a,b,L,check=FALSE,lmax=NULL,nsim=1)
Arguments
lambda |
intensity of the point process. it can be either a number, function of location and time, or an abject of class |
a |
lower bound of time period |
b |
upper bound of time period |
L |
a linear network |
check |
logical value indicating whether to check that all the (x,y) points lie inside the specified window. see |
lmax |
upper bound for the values of |
nsim |
number of simulated patterns to generate |
Details
This function generates realisations of a spatio-temporal poisson point process on a linear network based on an intensity function lambda and lower/upper bounds a and b.
Value
an object of class stlpp if nsim=1, otherwise a list of objects of class stlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
Examples
X <- rpoistlpp(0.2,a=0,b=5,L=easynet)
X
Simulating one-dimensional Poisson point patterns
Description
This function simulates realisations of an one-dimensional Poisson point process.
Usage
rpoistpp(lambda,a,b,check=FALSE,lmax=NULL,nsim=1)
Arguments
lambda |
intensity of the point process. it can be either a number, a function of location and time, or an object of class |
a |
lower bound of time period |
b |
upper bound of time period |
check |
logical value indicating whether to check that all the (x,y) points lie inside the specified time period. |
lmax |
upper bound for the values of |
nsim |
number of simulated patterns to generate |
Details
This function generates realisations of a temporal poisson point process based on a given intensity function lambda and lower/upper bounds a and b.
Value
an object of class tpp if nsim=1, otherwise a list of objects of class tpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
Examples
f <- function(t){0.1*exp(t)}
X <- rpoistpp(f,a=1,b=10)
Random thinning
Description
This function applies independent random thinning to a spatio-temporal point pattern on a linear network.
Usage
## S3 method for class 'stlpp'
rthin(X, P = P, nsim = 1)
Arguments
X |
a spatio-temporal point pattern of class |
P |
retention probability |
nsim |
number of simulated realisations to be generated |
Details
See rthin.
Value
An object of the same kind as X if nsim=1, or a list of such objects if nsim > 1.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
stlpp, rthin
Examples
data(Medellin)
rthin(Medellin,P=.5)
Create spatio-temporal point pattern on linear network
Description
Create an object of class stlpp representing a spatio-temporal point pattern on a linear network.
Usage
stlpp(X, L, T, ...)
Arguments
X |
Locations of the points. a matrix or data frame of coordinates, or a point pattern object (of class "ppp") or other data acceptable to |
L |
linear network (object of class |
T |
time occurrence of the points |
... |
ignored |
Details
This function creates an object of class stlpp. For details about X see lpp. T represents the time occurrences of data points.
Value
An object of class stlpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
See Also
as.stlpp, lpp
Examples
data(easynet)
X <- rpoislpp(1,easynet)
t <- runif(npoints(X))
stlpp(X,T=t,L=easynet)
Create a temporal point pattern
Description
Create an object of class tpp representing a one-dimensional point pattern.
Usage
tpp(X,a,b)
Arguments
X |
|
a |
lower band of the time domain. if not given by the user, it will be the minimum of X |
b |
upper bound of the time domain. if not given by the user, it will be the maximum of X |
Details
Create a one-dimensional point pattern.
Value
An object of class tpp.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
See Also
Examples
tpp(runif(10))
Extract unique points from a spatio-temporal point pattern on a linear network
Description
This function extracts unique points from a spatio-temporal point pattern on a linear network.
Usage
## S3 method for class 'stlpp'
unique(x,...)
Arguments
x |
a spatio-temporal point pattern of class |
... |
arguments for |
Details
This function extracts unique points from a spatio-temporal point pattern on a linear network.
Value
A spatio-temporal point pattern on a linear network with no duplicated point.
Author(s)
Mehdi Moradi <m2.moradi@yahoo.com>
References
Moradi, M., & 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
Examples
X <- rpoistlpp(0.1,0,5,L=easynet)
df <- as.data.frame(X)
df_dup <- df[sample(nrow(df), 20,replace = TRUE), ]
Y <- as.stlpp(df_dup,L=easynet)
npoints(Y)
npoints(unique(Y))