spatstat.linnet-package {spatstat.linnet}

The spatstat.linnet Package

Description

The spatstat.linnet package belongs to the spatstat family of packages. It contains the functionality for analysing spatial data on a linear network.

Details

spatstat is a family of R packages for the statistical analysis of spatial data. Its main focus is the analysis of spatial patterns of points in two-dimensional space.

The original spatstat package has now been split into several sub-packages.

This sub-package spatstat.linnet contains the user-level functions from spatstat that are concerned with spatial data on a linear network.

Structure of the spatstat family

The orginal spatstat package grew to be very large. It has now been divided into several sub-packages:

• spatstat.utils containing basic utilities

• spatstat.sparse containing linear algebra utilities

• spatstat.data containing datasets

• spatstat.geom containing geometrical objects and geometrical operations

• spatstat.explore containing the main functionality for exploratory and non-parametric analysis of spatial data

• spatstat.model containing the main functionality for statistical modelling and inference for spatial data

• spatstat.linnet containing functions for spatial data on a linear network

• spatstat, which simply loads the other sub-packages listed above, and provides documentation.

When you install spatstat, these sub-packages are also installed. Then if you load the spatstat package by typing library(spatstat), the other sub-packages listed above will automatically be loaded or imported. For an overview of all the functions available in these sub-packages, see the help file for spatstat in the spatstat package,

Additionally there are several extension packages:

• spatstat.gui for interactive graphics

• spatstat.local for local likelihood (including geographically weighted regression)

• spatstat.Knet for additional, computationally efficient code for linear networks

• spatstat.sphere (under development) for spatial data on a sphere, including spatial data on the earth's surface

The extension packages must be installed separately and loaded explicitly if needed. They also have separate documentation.

Overview of spatstat.linnet

A linear network is a subset of the two-dimensional plane composed of straight line segments. It could represent a road network, for example. Our code requires that, if two segments intersect each other, then the intersection is a single point, and the intersection point is treated as a vertex of the network.

The spatstat.linnet package supports spatial data analysis on a linear network. The primary aim is to analyse spatial patterns of points on a network. The points could represent road accidents on a road network, for example.

The spatstat.linnet package provides code for handling

• linear networks

• point patterns on a linear network

• pixel images on a linear network (where the network is divided into small segments and a numerical value is assigned to each segment)

• functions on a linear network (i.e. functions that are defined at every location along the network)

• tessellations of a linear network (where the network is subdivided into disjoint subsets with different labels)

• point process models on a linear network

Here is a list of the main functionality provided in spatstat.linnet.

Linear networks

An object of class "linnet" represents a linear network. Examples of such objects include the dataset simplenet provided in the package.

Linear network objects can be created by the following functions:

linnet	create a linear network
as.linnet	convert other data to a network
delaunayNetwork	network of Delaunay triangulation
dirichletNetwork	network of Dirichlet edges

Utilities for manipulating networks include:

[.linnet	extract subset of linear network
clickjoin	interactively join vertices in network
joinVertices	join existing vertices in a network
insertVertices	insert new vertices at positions along network
addVertices	add new vertices, extending a network
thinNetwork	remove vertices or lines from a network
repairNetwork	repair internal format
vertices.linnet	extract the vertices of network
terminalvertices	find terminal vertices of network
affine.linnet	apply affine transformation
shift.linnet	apply vector translation
rotate.linnet	apply rotation
rescale.linnet	rescale the unit of length
scalardilate.linnet	physically rescale the network
diameter.linnet	diameter of linear network
is.connected.linnet	determine whether network is connected
lineardisc	compute disc of given radius in network
marks.linnet	extract marks of a network
marks<-.linnet	assign marks to a network
plot.linnet	plot a network
as.owin.linnet	extract window containing network
as.psp.linnet	extract line segments comprising network
nsegments.linnet	number of segments in network
nvertices.linnet	number of vertices in network
pixellate.linnet	convert network to 2D pixel image
print.linnet	print basic information
summary.linnet	print summary information
unitname.linnet	extract name of unit of length
unitname<-.linnet	assign name of unit of length
vertexdegree	number of segments meeting each vertex
volume.linnet	total length of network
Window.linnet	extract window containing network
density.linnet	smoothed 2D spatial density of lines

A network is called a tree if it has no closed loops. The following functions support the creation and manipulation of trees:

begins	check start of character string
branchlabelfun	tree branch membership labelling function
deletebranch	delete a branch of a tree
extractbranch	extract a branch of a tree
treebranchlabels	label vertices of a tree by branch membership
treeprune	prune tree to given level

Point patterns on a linear network

An object of class "lpp" represents a point pattern on a linear network (for example, road accidents on a road network).

Examples of such objects include the following datasets provided with the package:

chicago	Chicago crime data
dendrite	Dendritic spines data
spiders	Spider webs on mortar lines of brick wall

Point patterns on a network can be created by the following functions:

lpp	create a point pattern on a linear network
as.lpp	convert other data to point pattern on network
clicklpp	interactively add points on a linear Network
crossing.linnet	crossing points between network and other lines

Point patterns on a network can be generated randomly using the following functions:

rpoislpp	Poisson points on linear network
runiflpp	uniform random points on a linear network
rlpp	random points on a linear network
rSwitzerlpp	simulate Switzer-type point process on linear network
rThomaslpp	simulate Thomas process on linear network
rcelllpp	simulate cell process on linear network
rjitter.lpp	randomly perturb a point pattern on a network

Functions for manipulating a point pattern on a network include the following. An object of class "lpp" also belongs to the class "ppx", for which additional support is available.

as.ppp.lpp	convert to 2D point pattern
as.psp.lpp	extract line segments
marks.ppx	extract marks associated with points
marks<-.ppx	assign marks to points on network
nsegments.lpp	count number of segments
print.lpp	print basic information
summary.lpp	print summary information
unitname.lpp	extract name of unit of length
unitname<-.lpp	assign name of unit of length
unmark.lpp	remove marks
subset.lpp	subset of points satisfying a condition
[.lpp	extract subset of point pattern
Window.lpp	extract window containing network
as.owin.lpp	extract window containing network
affine.lpp	apply affine transformation
shift.lpp	apply vector translation
rotate.lpp	apply rotation
rescale.lpp	rescale the unit of length
scalardilate.lpp	physically rescale the network and points
connected.lpp	find connected components of point pattern on network
cut.lpp	classify points in a Point Pattern on a Network
distfun.lpp	distance map (function)
distmap.lpp	distance map (image)
domain.lpp	extract the linear network
identify.lpp	interactively identify points
is.multitype.lpp	recognize whether point pattern is multitype
nncross.lpp	nearest neighbours
nndist.lpp	nearest neighbour distances
nnfromvertex	nearest data point from each vertex
nnfun.lpp	nearest neighbour map
nnwhich.lpp	identify nearest neighbours
pairdist.lpp	pairwise shortest-path distances
plot.lpp	plot point pattern on linear Network
points.lpp	draw points on existing plot
superimpose.lpp	superimpose several point patterns
text.lpp	add text labels
unstack.lpp	separate multiple columns of marks

Pixel images on a network

An object of class "linim" represents a pixel image on a linear network. Effectively, the network is divided into small segments (lixels) and each small segment is assigned a value, which could be numeric, factor, logical or complex values.

Pixel images on a network can be created using the following functions:

linim	create pixel image on linear network
as.linim	convert other data to pixel image on network

Functions for manipulating a pixel image on a network include:

[.linim	extract subset of pixel image on linear network
[<-.linim	reset values in subset of image on linear network
Math.linim	S3 group generic methods for images on a linear network
eval.linim	evaluate expression involving pixel images on linear network
as.linnet.linim	extract linear network
integral.linim	integral of pixel image on a linear network
mean.linim	mean of pixel values
median.linim	median of pixel values
quantile.linim	quantiles of pixel values
as.data.frame.linim	convert to data frame
print.linim	print basic information
summary.linim	print summary information
affine.linim	apply affine transformation
scalardilate.linim	apply scalar dilation
shift.linim	apply vector translation
pairs.linim	scatterplot matrix for images
persp.linim	perspective view of pixel image on network
plot.linim	plot pixel image on linear network

Functions on a linear network

An object of class "linfun" represents a function defined at any location along the network. Objects of this class are created by the following functions:

linfun	create function on a linear network
as.linfun	convert other data to function on network

The following supporting code is available:

print.linfun	print basic information
summary.linfun	print summary information
plot.linfun	plot function on network
persp.linfun	perspective view of function on network
as.data.frame.linfun	convert to data frame
as.owin.linfun	extract window containing network
as.function.linfun	convert to ordinary R function

Tessellations of a linear network

An object of class "lintess" represents a tessellation of the network, that is, a subdivision of the network into disjoint subsets called ‘tiles’. Objects of this class are created by the following functions:

lintess	create tessellation of network
chop.linnet	divide a linear network into tiles using infinite lines
divide.linnet	divide linear network at cut points
lineardirichlet	Dirichlet tessellation on a linear network

The following functions are provided for manipulating a tessellation on a network:

as.data.frame.lintess	convert to data frame
intersect.lintess	intersection of two tessellations on network
lineartileindex	determine which tile contains each given point on network
marks.lintess	extract marks of each tile
marks<-.lintess	assign marks to each tile
plot.lintess	plot tessellation on network
tile.lengths	compute lengths of tiles
tilenames.lintess	names of tiles
as.linfun.lintess	convert tessellation to a function

Smoothing a point pattern on a linear network:

Given a point pattern dataset on a linear network, it is often desired to estimate the spatially-varying density or intensity of points along the network. For example if the points represent road accidents, then we may wish to estimate the spatially-varying density of accidents per unit length (over a given period of time).

Related tasks include estimation of relative risk, and smoothing of of values observed at the data points.

density.lpp	kernel estimate of intensity
densityEqualSplit	kernel estimate of intensity using equal-split algorithm
densityHeat.lpp	kernel estimate of intensity using heat equation
densityQuick.lpp	kernel estimate of intensity using a 2D kernel
densityVoronoi.lpp	intensity estimate using Voronoi-Dirichlet Tessellation
densityfun.lpp	kernel estimate of intensity as a function
bw.lppl	Bandwidth selection for kernel estimate of intensity
bw.voronoi	bandwidth selection for Voronoi estimator
relrisk.lpp	kernel estimate of relative risk
bw.relrisk.lpp	Bandwidth selection for relative risk
Smooth.lpp	spatial smoothing of observations at points

Exploration of dependence on a covariate:

Another task is to investigate how the spatially-varying intensity of points depends on an explanatory variable (covariate). The covariate may be given as a pixel image on the network (class "linim") or as a function on the network (class "linfun").

rhohat.lpp	nonparametric estimate of intensity as function of a covariate
roc.lpp	Receiver Operating Characteristic for data on a network
auc.lpp	Area Under ROC Curve for data on a network
cdf.test.lpp	spatial distribution test for points on a linear network
berman.test.lpp	Berman's tests for point pattern on a network
sdr.lpp	Sufficient Dimension Reduction for a point pattern on a linear network

Summary statistics for a point pattern on a linear network:

These are for point patterns on a linear network (class lpp). For unmarked patterns:

linearK	K function on linear network
linearKinhom	inhomogeneous K function on linear network
linearpcf	pair correlation function on linear network
linearpcfinhom	inhomogeneous pair correlation on linear network
linearJinhom	inhomogeneous J function on linear network
linearKEuclid	K function on linear network using Euclidean distance
linearKEuclidInhom	inhomogeneous K function on linear network using Euclidean distance
linearpcfEuclid	pair correlation function on linear network using Euclidean distance
linearpcfEuclidInhom	inhomogeneous pair correlation on linear network using Euclidean distance

For multitype patterns:

linearKcross	K function between two types of points
linearKdot	K function from one type to any type
linearKcross.inhom	Inhomogeneous version of linearKcross
linearKdot.inhom	Inhomogeneous version of linearKdot
linearmarkconnect	Mark connection function on linear network
linearmarkequal	Mark equality function on linear network
linearpcfcross	Pair correlation between two types of points
linearpcfdot	Pair correlation from one type to any type
linearpcfcross.inhom	Inhomogeneous version of linearpcfcross
linearpcfdot.inhom	Inhomogeneous version of linearpcfdot

Related facilities:

pairdist.lpp	distances between pairs
crossdist.lpp	distances between pairs
nndist.lpp	nearest neighbour distances
nncross.lpp	nearest neighbour distances
nnwhich.lpp	find nearest neighbours
nnfun.lpp	find nearest data point
density.lpp	kernel smoothing estimator of intensity
distfun.lpp	distance transform
envelope.lpp	simulation envelopes
rpoislpp	simulate Poisson points on linear network
runiflpp	simulate random points on a linear network

It is also possible to fit point process models to lpp objects.

Point process models on a linear network:

An object of class "lpp" represents a pattern of points on a linear network. Point process models can also be fitted to these objects. Currently only Poisson models can be fitted.

lppm	point process model on linear network
anova.lppm	analysis of deviance for
	point process model on linear network
envelope.lppm	simulation envelopes for
	point process model on linear network
fitted.lppm	fitted intensity values
predict.lppm	model prediction on linear network
data.lppm	extract original data
berman.test.lppm	Berman's tests of goodness-of-fit
is.marked.lppm	Recognise whether model is marked
is.multitype.lppm	Recognise whether model is multitype
is.stationary.lppm	Recognise whether model is stationary
model.frame.lppm	Extract the variables in model
model.images.lppm	Compute images of constructed covariates
model.matrix.lppm	Extract design matrix
plot.lppm	Plot fitted point process model
pseudoR2.lppm	Calculate Pseudo-R-Squared for model
simulate.lppm	simulate fitted point process model

Licence

This library and its documentation are usable under the terms of the "GNU General Public License", a copy of which is distributed with the package.

Acknowledgements

Ottmar Cronie, Tilman Davies, Greg McSwiggan and Suman Rakshit made substantial contributions of code.

Author(s)

Adrian Baddeley [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail].