spatstat (version 1.46-1)

spatstat-package: The Spatstat Package

Description

This is a summary of the features of spatstat, a package in R for the statistical analysis of spatial point patterns.

Arguments

Getting Started

For a quick introduction to spatstat, read the package vignette Getting started with spatstat installed with spatstat. To read that document, you can either
  • visit cran.r-project.org/web/packages/spatstat and click on Getting Started with Spatstat
  • start R, type library(spatstat) and vignette('getstart')
  • start R, type help.start() to open the help browser, and navigate to Packages > spatstat > Vignettes.
Once you have installed spatstat, start R and type library(spatstat). Then type beginner for a beginner's introduction, or demo(spatstat) for a demonstration of the package's capabilities. For a complete course on spatstat, and on statistical analysis of spatial point patterns, read the book by Baddeley, Rubak and Turner (2015). Other recommended books on spatial point process methods are Diggle (2014), Gelfand et al (2010) and Illian et al (2008). The spatstat package includes over 50 datasets, which can be useful when learning the package. Type demo(data) to see plots of all datasets available in the package. Type vignette('datasets') for detailed background information on these datasets, and plots of each dataset. For information on converting your data into spatstat format, read Chapter 3 of Baddeley, Rubak and Turner (2015). This chapter is available free online, as one of the sample chapters at the book companion website, spatstat.github.io/book. For information about handling data in shapefiles, see Chapter 3, or the Vignette Handling shapefiles in the spatstat package, installed with spatstat, accessible as vignette('shapefiles').

Updates

New versions of spatstat are released every 8 weeks. Users are advised to update their installation of spatstat regularly. Type latest.news to read the news documentation about changes to the current installed version of spatstat. See the Vignette Summary of recent updates, installed with spatstat, which describes the main changes to spatstat since the book (Baddeley, Rubak and Turner, 2015) was published. It is accessible as vignette('updates'). Type news(package="spatstat") to read news documentation about all previous versions of the package.

FUNCTIONS AND DATASETS

Following is a summary of the main functions and datasets in the spatstat package. Alternatively an alphabetical list of all functions and datasets is available by typing library(help=spatstat). For further information on any of these, type help(name) or ?name where name is the name of the function or dataset.

CONTENTS:

I.
Creating and manipulating data
II.
Exploratory Data Analysis
III.
Model fitting (Cox and cluster models)
IV.
Model fitting (Poisson and Gibbs models)
V.
Model fitting (determinantal point processes)
VI.
Model fitting (spatial logistic regression)
VII.
Simulation
VIII.
Tests and diagnostics

I. CREATING AND MANIPULATING DATA

Types of spatial data: The main types of spatial data supported by spatstat are:
ppp
point pattern
owin
window (spatial region)
im
pixel image
psp
line segment pattern
tess
tessellation
pp3
three-dimensional point pattern
ppx
point pattern in any number of dimensions
To create a point pattern:
ppp
create a point pattern from $(x,y)$ and window information
ppp(x, y, xlim, ylim) for rectangular window
ppp(x, y, poly) for polygonal window
ppp(x, y, mask) for binary image window
as.ppp
convert other types of data to a ppp object
clickppp
interactively add points to a plot
To simulate a random point pattern:
runifpoint
generate $n$ independent uniform random points
rpoint
generate $n$ independent random points
rmpoint
generate $n$ independent multitype random points
rpoispp
simulate the (in)homogeneous Poisson point process
rmpoispp
simulate the (in)homogeneous multitype Poisson point process
runifdisc
generate $n$ independent uniform random points in disc
rstrat
stratified random sample of points
rsyst
systematic random sample of points
rjitter
apply random displacements to points in a pattern
rMaternI
simulate the Matern Model I inhibition process
rMaternII
simulate the Matern Model II inhibition process
rSSI
simulate Simple Sequential Inhibition process
rStrauss
simulate Strauss process (perfect simulation)
rHardcore
simulate Hard Core process (perfect simulation)
rStraussHard
simulate Strauss-hard core process (perfect simulation)
rDiggleGratton
simulate Diggle-Gratton process (perfect simulation)
rDGS
simulate Diggle-Gates-Stibbard process (perfect simulation)
rPenttinen
simulate Penttinen process (perfect simulation)
rNeymanScott
simulate a general Neyman-Scott process
rPoissonCluster
simulate a general Poisson cluster process
rMatClust
simulate the Matern Cluster process
rThomas
simulate the Thomas process
rGaussPoisson
simulate the Gauss-Poisson cluster process
rCauchy
simulate Neyman-Scott Cauchy cluster process
rVarGamma
simulate Neyman-Scott Variance Gamma cluster process
rthin
random thinning
rcell
simulate the Baddeley-Silverman cell process
rmh
simulate Gibbs point process using Metropolis-Hastings
simulate.ppm
simulate Gibbs point process using Metropolis-Hastings
runifpointOnLines
generate $n$ random points along specified line segments
To randomly change an existing point pattern:
rshift
random shifting of points
rjitter
apply random displacements to points in a pattern
rthin
random thinning
rlabel
random (re)labelling of a multitype point pattern
Standard point pattern datasets: Datasets in spatstat are lazy-loaded, so you can simply type the name of the dataset to use it; there is no need to type data(amacrine) etc. Type demo(data) to see a display of all the datasets installed with the package. Type vignette('datasets') for a document giving an overview of all datasets, including background information, and plots.
amacrine
Austin Hughes' rabbit amacrine cells
anemones
Upton-Fingleton sea anemones data
ants
Harkness-Isham ant nests data
bdspots
Breakdown spots in microelectrodes
bei
Tropical rainforest trees
betacells
Waessle et al. cat retinal ganglia data
bramblecanes
Bramble Canes data
bronzefilter
Bronze Filter Section data
cells
Crick-Ripley biological cells data
chicago
Chicago street crimes
chorley
Chorley-Ribble cancer data
clmfires
Castilla-La Mancha forest fires
copper
Berman-Huntington copper deposits data
dendrite
Dendritic spines
demohyper
Synthetic point patterns
demopat
Synthetic point pattern
finpines
Finnish Pines data
flu
Influenza virus proteins
gordon
People in Gordon Square, London
gorillas
Gorilla nest sites
hamster
Aherne's hamster tumour data
humberside
North Humberside childhood leukaemia data
hyytiala
Mixed forest in Hyytiala, Finland
japanesepines
Japanese Pines data
lansing
Lansing Woods data
longleaf
Longleaf Pines data
mucosa
Cells in gastric mucosa
murchison
Murchison gold deposits
nbfires
New Brunswick fires data
nztrees
Mark-Esler-Ripley trees data
osteo
Osteocyte lacunae (3D, replicated)
paracou
Kimboto trees in Paracou, French Guiana
ponderosa
Getis-Franklin ponderosa pine trees data
pyramidal
Pyramidal neurons from 31 brains
redwood
Strauss-Ripley redwood saplings data
redwoodfull
Strauss redwood saplings data (full set)
residualspaper
Data from Baddeley et al (2005)
shapley
Galaxies in an astronomical survey
simdat
Simulated point pattern (inhomogeneous, with interaction)
spiders
Spider webs on mortar lines of brick wall
sporophores
Mycorrhizal fungi around a tree
spruces
Spruce trees in Saxonia
swedishpines
Strand-Ripley Swedish pines data
urkiola
Urkiola Woods data
waka
Trees in Waka national park
To manipulate a point pattern:
plot.ppp
plot a point pattern (e.g. plot(X))
iplot
plot a point pattern interactively
edit.ppp
interactive text editor
[.ppp
extract or replace a subset of a point pattern
pp[subset] or pp[subwindow]
subset.ppp
extract subset of point pattern satisfying a condition
superimpose
combine several point patterns
by.ppp
apply a function to sub-patterns of a point pattern
cut.ppp
classify the points in a point pattern
split.ppp
divide pattern into sub-patterns
unmark
remove marks
npoints
count the number of points
coords
extract coordinates, change coordinates
marks
extract marks, change marks or attach marks
rotate
rotate pattern
shift
translate pattern
flipxy
swap $x$ and $y$ coordinates
reflect
reflect in the origin
periodify
make several translated copies
affine
apply affine transformation
scalardilate
apply scalar dilation
density.ppp
kernel estimation of point pattern intensity
Smooth.ppp
kernel smoothing of marks of point pattern
nnmark
mark value of nearest data point
sharpen.ppp
data sharpening
identify.ppp
interactively identify points
unique.ppp
remove duplicate points
duplicated.ppp
determine which points are duplicates
connected.ppp
find clumps of points
dirichlet
compute Dirichlet-Voronoi tessellation
delaunay
compute Delaunay triangulation
delaunayDistance
graph distance in Delaunay triangulation
convexhull
compute convex hull
discretise
discretise coordinates
pixellate.ppp
approximate point pattern by pixel image
See spatstat.options to control plotting behaviour. To create a window: An object of class "owin" describes a spatial region (a window of observation).
owin
Create a window object
owin(xlim, ylim) for rectangular window
owin(poly) for polygonal window
owin(mask) for binary image window
Window
Extract window of another object
Frame
Extract the containing rectangle ('frame') of another object
as.owin
Convert other data to a window object
square
make a square window
disc
make a circular window
ellipse
make an elliptical window
ripras
Ripley-Rasson estimator of window, given only the points
convexhull
compute convex hull of something
letterR
polygonal window in the shape of the R logo
clickpoly
interactively draw a polygonal window
To manipulate a window:
plot.owin
plot a window.
plot(W)
boundingbox
Find a tight bounding box for the window
erosion
erode window by a distance r
dilation
dilate window by a distance r
closing
close window by a distance r
opening
open window by a distance r
border
difference between window and its erosion/dilation
complement.owin
invert (swap inside and outside)
simplify.owin
approximate a window by a simple polygon
rotate
rotate window
flipxy
swap $x$ and $y$ coordinates
shift
translate window
periodify
make several translated copies
affine
apply affine transformation
Digital approximations:
as.mask
Make a discrete pixel approximation of a given window
as.im.owin
convert window to pixel image
pixellate.owin
convert window to pixel image
commonGrid
find common pixel grid for windows
nearest.raster.point
map continuous coordinates to raster locations
raster.x
raster x coordinates
raster.y
raster y coordinates
raster.xy
raster x and y coordinates
See spatstat.options to control the approximation Geometrical computations with windows:
edges
extract boundary edges
intersect.owin
intersection of two windows
union.owin
union of two windows
setminus.owin
set subtraction of two windows
inside.owin
determine whether a point is inside a window
area.owin
compute area
perimeter
compute perimeter length
diameter.owin
compute diameter
incircle
find largest circle inside a window
inradius
radius of incircle
connected.owin
find connected components of window
eroded.areas
compute areas of eroded windows
dilated.areas
compute areas of dilated windows
bdist.points
compute distances from data points to window boundary
bdist.pixels
compute distances from all pixels to window boundary
bdist.tiles
boundary distance for each tile in tessellation
distmap.owin
distance transform image
distfun.owin
distance transform
centroid.owin
compute centroid (centre of mass) of window
is.subset.owin
determine whether one window contains another
is.convex
determine whether a window is convex
convexhull
compute convex hull
triangulate.owin
decompose into triangles
as.mask
pixel approximation of window
as.polygonal
polygonal approximation of window
is.rectangle
test whether window is a rectangle
is.polygonal
test whether window is polygonal
is.mask
test whether window is a mask
setcov
spatial covariance function of window
pixelcentres
extract centres of pixels in mask
Pixel images: An object of class "im" represents a pixel image. Such objects are returned by some of the functions in spatstat including Kmeasure, setcov and density.ppp.
im
create a pixel image
as.im
convert other data to a pixel image
pixellate
convert other data to a pixel image
as.matrix.im
convert pixel image to matrix
as.data.frame.im
convert pixel image to data frame
as.function.im
convert pixel image to function
plot.im
plot a pixel image on screen as a digital image
contour.im
draw contours of a pixel image
persp.im
draw perspective plot of a pixel image
rgbim
create colour-valued pixel image
hsvim
create colour-valued pixel image
[.im
extract a subset of a pixel image
[<-.im
replace a subset of a pixel image
rotate.im
rotate pixel image
shift.im
apply vector shift to pixel image
affine.im
apply affine transformation to image
X
print very basic information about image X
summary(X)
summary of image X
hist.im
histogram of image
mean.im
mean pixel value of image
integral.im
integral of pixel values
quantile.im
quantiles of image
cut.im
convert numeric image to factor image
is.im
test whether an object is a pixel image
interp.im
interpolate a pixel image
blur
apply Gaussian blur to image
Smooth.im
apply Gaussian blur to image
connected.im
find connected components
compatible.im
test whether two images have compatible dimensions
harmonise.im
make images compatible
commonGrid
find a common pixel grid for images
eval.im
evaluate any expression involving images
scaletointerval
rescale pixel values
zapsmall.im
set very small pixel values to zero
levelset
level set of an image
solutionset
region where an expression is true
imcov
spatial covariance function of image
convolve.im
spatial convolution of images
transect.im
line transect of image
pixelcentres
extract centres of pixels
transmat
convert matrix of pixel values
to a different indexing convention
Line segment patterns An object of class "psp" represents a pattern of straight line segments.
psp
create a line segment pattern
as.psp
convert other data into a line segment pattern
edges
extract edges of a window
is.psp
determine whether a dataset has class "psp"
plot.psp
plot a line segment pattern
print.psp
print basic information
summary.psp
print summary information
[.psp
extract a subset of a line segment pattern
as.data.frame.psp
convert line segment pattern to data frame
marks.psp
extract marks of line segments
marks<-.psp
assign new marks to line segments
unmark.psp
delete marks from line segments
midpoints.psp
compute the midpoints of line segments
endpoints.psp
extract the endpoints of line segments
lengths.psp
compute the lengths of line segments
angles.psp
compute the orientation angles of line segments
superimpose
combine several line segment patterns
flipxy
swap $x$ and $y$ coordinates
rotate.psp
rotate a line segment pattern
shift.psp
shift a line segment pattern
periodify
make several shifted copies
affine.psp
apply an affine transformation
pixellate.psp
approximate line segment pattern by pixel image
as.mask.psp
approximate line segment pattern by binary mask
distmap.psp
compute the distance map of a line segment pattern
distfun.psp
compute the distance map of a line segment pattern
density.psp
kernel smoothing of line segments
selfcrossing.psp
find crossing points between line segments
selfcut.psp
cut segments where they cross
crossing.psp
find crossing points between two line segment patterns
nncross
find distance to nearest line segment from a given point
nearestsegment
find line segment closest to a given point
project2segment
find location along a line segment closest to a given point
pointsOnLines
generate points evenly spaced along line segment
rpoisline
generate a realisation of the Poisson line process inside a window
Tessellations An object of class "tess" represents a tessellation.
tess
create a tessellation
quadrats
create a tessellation of rectangles
hextess
create a tessellation of hexagons
quantess
quantile tessellation
as.tess
convert other data to a tessellation
plot.tess
plot a tessellation
tiles
extract all the tiles of a tessellation
[.tess
extract some tiles of a tessellation
[<-.tess
change some tiles of a tessellation
intersect.tess
intersect two tessellations
or restrict a tessellation to a window
chop.tess
subdivide a tessellation by a line
dirichlet
compute Dirichlet-Voronoi tessellation of points
delaunay
compute Delaunay triangulation of points
rpoislinetess
generate tessellation using Poisson line process
tile.areas
area of each tile in tessellation
Three-dimensional point patterns An object of class "pp3" represents a three-dimensional point pattern in a rectangular box. The box is represented by an object of class "box3".
pp3
create a 3-D point pattern
plot.pp3
plot a 3-D point pattern
coords
extract coordinates
as.hyperframe
extract coordinates
subset.pp3
extract subset of 3-D point pattern
unitname.pp3
name of unit of length
npoints
count the number of points
runifpoint3
generate uniform random points in 3-D
rpoispp3
generate Poisson random points in 3-D
envelope.pp3
generate simulation envelopes for 3-D pattern
box3
create a 3-D rectangular box
as.box3
convert data to 3-D rectangular box
unitname.box3
name of unit of length
diameter.box3
diameter of box
volume.box3
volume of box
shortside.box3
shortest side of box
Multi-dimensional space-time point patterns An object of class "ppx" represents a point pattern in multi-dimensional space and/or time.
ppx
create a multidimensional space-time point pattern
coords
extract coordinates
as.hyperframe
extract coordinates
subset.ppx
extract subset
unitname.ppx
name of unit of length
npoints
count the number of points
runifpointx
generate uniform random points
rpoisppx
generate Poisson random points
boxx
define multidimensional box
diameter.boxx
diameter of box
volume.boxx
volume of box
shortside.boxx
shortest side of box
Point patterns on a linear network An object of class "linnet" represents a linear network (for example, a road network).
linnet
create a linear network
clickjoin
interactively join vertices in network
iplot.linnet
interactively plot network
simplenet
simple example of network
lineardisc
disc in a linear network
delaunayNetwork
network of Delaunay triangulation
dirichletNetwork
network of Dirichlet edges
methods.linnet
methods for linnet objects
vertices.linnet
nodes of network
An object of class "lpp" represents a point pattern on a linear network (for example, road accidents on a road network).
lpp
create a point pattern on a linear network
methods.lpp
methods for lpp objects
subset.lpp
method for subset
rpoislpp
simulate Poisson points on linear network
runiflpp
simulate random points on a linear network
chicago
Chicago street crime data
dendrite
Dendritic spines data
Hyperframes A hyperframe is like a data frame, except that the entries may be objects of any kind.
hyperframe
create a hyperframe
as.hyperframe
convert data to hyperframe
plot.hyperframe
plot hyperframe
with.hyperframe
evaluate expression using each row of hyperframe
cbind.hyperframe
combine hyperframes by columns
rbind.hyperframe
combine hyperframes by rows
as.data.frame.hyperframe
convert hyperframe to data frame
subset.hyperframe
method for subset
head.hyperframe
first few rows of hyperframe
Layered objects A layered object represents data that should be plotted in successive layers, for example, a background and a foreground.
layered
create layered object
plot.layered
plot layered object
Colour maps A colour map is a mechanism for associating colours with data. It can be regarded as a function, mapping data to colours. Using a colourmap object in a plot command ensures that the mapping from numbers to colours is the same in different plots.
colourmap
create a colour map
plot.colourmap
plot the colour map only
tweak.colourmap
alter individual colour values
interp.colourmap
make a smooth transition between colours

II. EXPLORATORY DATA ANALYSIS

Inspection of data:
summary(X)
print useful summary of point pattern X
X
print basic description of point pattern X
any(duplicated(X))
check for duplicated points in pattern X
istat(X)
Interactive exploratory analysis
Classical exploratory tools:
clarkevans
Clark and Evans aggregation index
fryplot
Fry plot
Smoothing:
density.ppp
kernel smoothed density/intensity
relrisk
kernel estimate of relative risk
Smooth.ppp
spatial interpolation of marks
bw.diggle
cross-validated bandwidth selection for density.ppp
bw.ppl
likelihood cross-validated bandwidth selection for density.ppp
bw.scott
Scott's rule of thumb for density estimation
bw.relrisk
cross-validated bandwidth selection for relrisk
bw.smoothppp
cross-validated bandwidth selection for Smooth.ppp
bw.frac
bandwidth selection using window geometry
Modern exploratory tools:
clusterset
Allard-Fraley feature detection
nnclean
Byers-Raftery feature detection
sharpen.ppp
Choi-Hall data sharpening
rhohat
Kernel estimate of covariate effect
rho2hat
Kernel estimate of effect of two covariates
spatialcdf
Spatial cumulative distribution function
Summary statistics for a point pattern: Type demo(sumfun) for a demonstration of many of the summary statistics.
intensity
Mean intensity
quadratcount
Quadrat counts
intensity.quadratcount
Mean intensity in quadrats
Fest
empty space function $F$
Gest
nearest neighbour distribution function $G$
Jest
$J$-function $J = (1-G)/(1-F)$
Kest
Ripley's $K$-function
Lest
Besag $L$-function
Tstat
Third order $T$-function
allstats
all four functions $F$, $G$, $J$, $K$
pcf
pair correlation function
Kinhom
$K$ for inhomogeneous point patterns
Linhom
$L$ for inhomogeneous point patterns
pcfinhom
pair correlation for inhomogeneous patterns
Finhom
$F$ for inhomogeneous point patterns
Ginhom
$G$ for inhomogeneous point patterns
Jinhom
$J$ for inhomogeneous point patterns
localL
Getis-Franklin neighbourhood density function
localK
neighbourhood K-function
localpcf
local pair correlation function
localKinhom
local $K$ for inhomogeneous point patterns
localLinhom
local $L$ for inhomogeneous point patterns
localpcfinhom
local pair correlation for inhomogeneous patterns
Ksector
Directional $K$-function
Kscaled
locally scaled $K$-function
Kest.fft
fast $K$-function using FFT for large datasets
Kmeasure
reduced second moment measure
envelope
simulation envelopes for a summary function
varblock
variances and confidence intervals
for a summary function
Related facilities:
plot.fv
plot a summary function
eval.fv
evaluate any expression involving summary functions
harmonise.fv
make functions compatible
eval.fasp
evaluate any expression involving an array of functions
with.fv
evaluate an expression for a summary function
Smooth.fv
apply smoothing to a summary function
deriv.fv
calculate derivative of a summary function
pool.fv
pool several estimates of a summary function
nndist
nearest neighbour distances
nnwhich
find nearest neighbours
pairdist
distances between all pairs of points
crossdist
distances between points in two patterns
nncross
nearest neighbours between two point patterns
exactdt
distance from any location to nearest data point
distmap
distance map image
distfun
distance map function
nnmap
nearest point image
nnfun
nearest point function
density.ppp
kernel smoothed density
Smooth.ppp
spatial interpolation of marks
relrisk
kernel estimate of relative risk
sharpen.ppp
data sharpening
Summary statistics for a multitype point pattern: A multitype point pattern is represented by an object X of class "ppp" such that marks(X) is a factor.
relrisk
kernel estimation of relative risk
scan.test
spatial scan test of elevated risk
Gcross,Gdot,Gmulti
multitype nearest neighbour distributions $G[i,j], G[i.]$
Kcross,Kdot, Kmulti
multitype $K$-functions $K[i,j], K[i.]$
Lcross,Ldot
multitype $L$-functions $L[i,j], L[i.]$
Jcross,Jdot,Jmulti
multitype $J$-functions $J[i,j],J[i.]$
pcfcross
multitype pair correlation function $g[i,j]$
pcfdot
multitype pair correlation function $g[i.]$
pcfmulti
general pair correlation function
markconnect
marked connection function $p[i,j]$
alltypes
estimates of the above for all $i,j$ pairs
Iest
multitype $I$-function
Kcross.inhom,Kdot.inhom
inhomogeneous counterparts of Kcross, Kdot
Lcross.inhom,Ldot.inhom
inhomogeneous counterparts of Lcross, Ldot
Summary statistics for a marked point pattern: A marked point pattern is represented by an object X of class "ppp" with a component X$marks. The entries in the vector X$marks may be numeric, complex, string or any other atomic type. For numeric marks, there are the following functions:
markmean
smoothed local average of marks
markvar
smoothed local variance of marks
markcorr
mark correlation function
markcrosscorr
mark cross-correlation function
markvario
mark variogram
Kmark
mark-weighted $K$ function
Emark
mark independence diagnostic $E(r)$
Vmark
mark independence diagnostic $V(r)$
nnmean
nearest neighbour mean index
For marks of any type, there are the following:
Gmulti
multitype nearest neighbour distribution
Kmulti
multitype $K$-function
Alternatively use cut.ppp to convert a marked point pattern to a multitype point pattern. Programming tools:
applynbd
apply function to every neighbourhood in a point pattern
markstat
apply function to the marks of neighbours in a point pattern
marktable
tabulate the marks of neighbours in a point pattern
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
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
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
It is also possible to fit point process models to lpp objects. See Section IV. Summary statistics for a three-dimensional point pattern: These are for 3-dimensional point pattern objects (class pp3).
F3est
empty space function $F$
G3est
nearest neighbour function $G$
K3est
$K$-function
Related facilities:
envelope.pp3
simulation envelopes
pairdist.pp3
distances between all pairs of points
crossdist.pp3
distances between points in two patterns
nndist.pp3
nearest neighbour distances
nnwhich.pp3
find nearest neighbours
Computations for multi-dimensional point pattern: These are for multi-dimensional space-time point pattern objects (class ppx).
pairdist.ppx
distances between all pairs of points
crossdist.ppx
distances between points in two patterns
nndist.ppx
nearest neighbour distances
Summary statistics for random sets: These work for point patterns (class ppp), line segment patterns (class psp) or windows (class owin).
Hest
spherical contact distribution $H$
Gfox
Foxall $G$-function

III. MODEL FITTING (COX AND CLUSTER MODELS)

Cluster process models (with homogeneous or inhomogeneous intensity) and Cox processes can be fitted by the function kppm. Its result is an object of class "kppm". The fitted model can be printed, plotted, predicted, simulated and updated.
kppm
Fit model
plot.kppm
Plot the fitted model
summary.kppm
Summarise the fitted model
fitted.kppm
Compute fitted intensity
predict.kppm
Compute fitted intensity
update.kppm
Update the model
improve.kppm
Refine the estimate of trend
simulate.kppm
Generate simulated realisations
vcov.kppm
Variance-covariance matrix of coefficients
coef.kppm
Extract trend coefficients
formula.kppm
Extract trend formula
parameters
Extract all model parameters
clusterfield
Compute offspring density
clusterradius
Radius of support of offspring density
Kmodel.kppm
$K$ function of fitted model
For model selection, you can also use the generic functions step, drop1 and AIC on fitted point process models. The theoretical models can also be simulated, for any choice of parameter values, using rThomas, rMatClust, rCauchy, rVarGamma, and rLGCP. Lower-level fitting functions include:
lgcp.estK
fit a log-Gaussian Cox process model
lgcp.estpcf
fit a log-Gaussian Cox process model
thomas.estK
fit the Thomas process model
thomas.estpcf
fit the Thomas process model
matclust.estK
fit the Matern Cluster process model
matclust.estpcf
fit the Matern Cluster process model
cauchy.estK
fit a Neyman-Scott Cauchy cluster process
cauchy.estpcf
fit a Neyman-Scott Cauchy cluster process
vargamma.estK
fit a Neyman-Scott Variance Gamma process
vargamma.estpcf
fit a Neyman-Scott Variance Gamma process
mincontrast
low-level algorithm for fitting models

IV. MODEL FITTING (POISSON AND GIBBS MODELS)

Types of models Poisson point processes are the simplest models for point patterns. A Poisson model assumes that the points are stochastically independent. It may allow the points to have a non-uniform spatial density. The special case of a Poisson process with a uniform spatial density is often called Complete Spatial Randomness. Poisson point processes are included in the more general class of Gibbs point process models. In a Gibbs model, there is interaction or dependence between points. Many different types of interaction can be specified. For a detailed explanation of how to fit Poisson or Gibbs point process models to point pattern data using spatstat, see Baddeley and Turner (2005b) or Baddeley (2008). To fit a Poisson or Gibbs point process model: Model fitting in spatstat is performed mainly by the function ppm. Its result is an object of class "ppm". Here are some examples, where X is a point pattern (class "ppp"):
command
model
ppm(X)
Complete Spatial Randomness
ppm(X ~ 1)
Complete Spatial Randomness
ppm(X ~ x)
Poisson process with
intensity loglinear in $x$ coordinate
ppm(X ~ 1, Strauss(0.1))
Stationary Strauss process
ppm(X ~ x, Strauss(0.1))
Strauss process with
It is also possible to fit models that depend on other covariates. Manipulating the fitted model:
plot.ppm
Plot the fitted model
predict.ppm
Compute the spatial trend and conditional intensity
of the fitted point process model
coef.ppm
Extract the fitted model coefficients
parameters
Extract all model parameters
formula.ppm
Extract the trend formula
intensity.ppm
Compute fitted intensity
Kmodel.ppm
$K$ function of fitted model
pcfmodel.ppm
pair correlation of fitted model
fitted.ppm
Compute fitted conditional intensity at quadrature points
residuals.ppm
Compute point process residuals at quadrature points
update.ppm
Update the fit
vcov.ppm
Variance-covariance matrix of estimates
rmh.ppm
Simulate from fitted model
simulate.ppm
Simulate from fitted model
print.ppm
Print basic information about a fitted model
summary.ppm
Summarise a fitted model
effectfun
Compute the fitted effect of one covariate
logLik.ppm
log-likelihood or log-pseudolikelihood
anova.ppm
Analysis of deviance
model.frame.ppm
Extract data frame used to fit model
model.images
Extract spatial data used to fit model
model.depends
Identify variables in the model
as.interact
Interpoint interaction component of model
fitin
Extract fitted interpoint interaction
is.hybrid
Determine whether the model is a hybrid
valid.ppm
Check the model is a valid point process
For model selection, you can also use the generic functions step, drop1 and AIC on fitted point process models. See spatstat.options to control plotting of fitted model. To specify a point process model: The first order ``trend'' of the model is determined by an R language formula. The formula specifies the form of the logarithm of the trend.
X ~ 1
No trend (stationary)
X ~ x
Loglinear trend $lambda(x,y) = exp(alpha + beta * x)$
where $x,y$ are Cartesian coordinates
X ~ polynom(x,y,3)
Log-cubic polynomial trend
X ~ harmonic(x,y,2)
Log-harmonic polynomial trend
X ~ Z
Loglinear function of covariate Z
The higher order (``interaction'') components are described by an object of class "interact". Such objects are created by:
Poisson()
the Poisson point process
AreaInter()
Area-interaction process
BadGey()
multiscale Geyer process
Concom()
connected component interaction
DiggleGratton()
Diggle-Gratton potential
DiggleGatesStibbard()
Diggle-Gates-Stibbard potential
Fiksel()
Fiksel pairwise interaction process
Geyer()
Geyer's saturation process
Hardcore()
Hard core process
HierHard()
Hierarchical multiype hard core process
HierStrauss()
Hierarchical multiype Strauss process
HierStraussHard()
Hierarchical multiype Strauss-hard core process
Hybrid()
Hybrid of several interactions
LennardJones()
Lennard-Jones potential
MultiHard()
multitype hard core process
MultiStrauss()
multitype Strauss process
MultiStraussHard()
multitype Strauss/hard core process
OrdThresh()
Ord process, threshold potential
Ord()
Ord model, user-supplied potential
PairPiece()
pairwise interaction, piecewise constant
Pairwise()
pairwise interaction, user-supplied potential
Penttinen()
Penttinen pairwise interaction
SatPiece()
Saturated pair model, piecewise constant potential
Saturated()
Saturated pair model, user-supplied potential
Softcore()
pairwise interaction, soft core potential
Strauss()
Strauss process
StraussHard()
Strauss/hard core point process
Note that it is also possible to combine several such interactions using Hybrid. Finer control over model fitting: A quadrature scheme is represented by an object of class "quad". To create a quadrature scheme, typically use quadscheme.
quadscheme
default quadrature scheme
using rectangular cells or Dirichlet cells
pixelquad
quadrature scheme based on image pixels
To inspect a quadrature scheme:
plot(Q)
plot quadrature scheme Q
print(Q)
print basic information about quadrature scheme Q
A quadrature scheme consists of data points, dummy points, and weights. To generate dummy points:
default.dummy
default pattern of dummy points
gridcentres
dummy points in a rectangular grid
rstrat
stratified random dummy pattern
spokes
radial pattern of dummy points
To compute weights:
gridweights
quadrature weights by the grid-counting rule
Simulation and goodness-of-fit for fitted models:
rmh.ppm
simulate realisations of a fitted model
simulate.ppm
simulate realisations of a fitted model
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
linim
pixel image on linear network
plot.linim
plot a pixel image on linear network
eval.linim
evaluate expression involving images
linfun
function defined on linear network

V. MODEL FITTING (DETERMINANTAL POINT PROCESS MODELS)

Code for fitting determinantal point process models has recently been added to spatstat. For information, see the help file for dppm.

VI. MODEL FITTING (SPATIAL LOGISTIC REGRESSION)

Logistic regression Pixel-based spatial logistic regression is an alternative technique for analysing spatial point patterns that is widely used in Geographical Information Systems. It is approximately equivalent to fitting a Poisson point process model. In pixel-based logistic regression, the spatial domain is divided into small pixels, the presence or absence of a data point in each pixel is recorded, and logistic regression is used to model the presence/absence indicators as a function of any covariates. Facilities for performing spatial logistic regression are provided in spatstat for comparison purposes. Fitting a spatial logistic regression Spatial logistic regression is performed by the function slrm. Its result is an object of class "slrm". There are many methods for this class, including methods for print, fitted, predict, simulate, anova, coef, logLik, terms, update, formula and vcov. For example, if X is a point pattern (class "ppp"):
command
model
slrm(X ~ 1)
Complete Spatial Randomness
slrm(X ~ x)
Poisson process with
intensity loglinear in $x$ coordinate
slrm(X ~ Z)
Poisson process with
Manipulating a fitted spatial logistic regression
anova.slrm
Analysis of deviance
coef.slrm
Extract fitted coefficients
vcov.slrm
Variance-covariance matrix of fitted coefficients
fitted.slrm
Compute fitted probabilities or intensity
logLik.slrm
Evaluate loglikelihood of fitted model
plot.slrm
Plot fitted probabilities or intensity
predict.slrm
Compute predicted probabilities or intensity with new data
There are many other undocumented methods for this class, including methods for print, update, formula and terms. Stepwise model selection is possible using step or stepAIC.

VII. SIMULATION

There are many ways to generate a random point pattern, line segment pattern, pixel image or tessellation in spatstat. Random point patterns:
runifpoint
generate $n$ independent uniform random points
rpoint
generate $n$ independent random points
rmpoint
generate $n$ independent multitype random points
rpoispp
simulate the (in)homogeneous Poisson point process
rmpoispp
simulate the (in)homogeneous multitype Poisson point process
runifdisc
generate $n$ independent uniform random points in disc
rstrat
stratified random sample of points
rsyst
systematic random sample (grid) of points
rMaternI
simulate the Matern Model I inhibition process
rMaternII
simulate the Matern Model II inhibition process
rSSI
simulate Simple Sequential Inhibition process
rHardcore
simulate hard core process (perfect simulation)
rStrauss
simulate Strauss process (perfect simulation)
rStraussHard
simulate Strauss-hard core process (perfect simulation)
rDiggleGratton
simulate Diggle-Gratton process (perfect simulation)
rDGS
simulate Diggle-Gates-Stibbard process (perfect simulation)
rPenttinen
simulate Penttinen process (perfect simulation)
rNeymanScott
simulate a general Neyman-Scott process
rMatClust
simulate the Matern Cluster process
rThomas
simulate the Thomas process
rLGCP
simulate the log-Gaussian Cox process
rGaussPoisson
simulate the Gauss-Poisson cluster process
rCauchy
simulate Neyman-Scott process with Cauchy clusters
rVarGamma
simulate Neyman-Scott process with Variance Gamma clusters
rcell
simulate the Baddeley-Silverman cell process
runifpointOnLines
generate $n$ random points along specified line segments
Resampling a point pattern:
quadratresample
block resampling
rjitter
apply random displacements to points in a pattern
rshift
random shifting of (subsets of) points
See also varblock for estimating the variance of a summary statistic by block resampling, and lohboot for another bootstrap technique. Fitted point process models: If you have fitted a point process model to a point pattern dataset, the fitted model can be simulated. Cluster process models are fitted by the function kppm yielding an object of class "kppm". To generate one or more simulated realisations of this fitted model, use simulate.kppm. Gibbs point process models are fitted by the function ppm yielding an object of class "ppm". To generate a simulated realisation of this fitted model, use rmh. To generate one or more simulated realisations of the fitted model, use simulate.ppm. Other random patterns:
rlinegrid
generate a random array of parallel lines through a window
rpoisline
simulate the Poisson line process within a window
rpoislinetess
generate random tessellation using Poisson line process
rMosaicSet
generate random set by selecting some tiles of a tessellation
Simulation-based inference
envelope
critical envelope for Monte Carlo test of goodness-of-fit
qqplot.ppm
diagnostic plot for interpoint interaction
scan.test
spatial scan statistic/test
studpermu.test
studentised permutation test

VIII. TESTS AND DIAGNOSTICS

Classical hypothesis tests:
quadrat.test
$chi^2$ goodness-of-fit test on quadrat counts
clarkevans.test
Clark and Evans test
cdf.test
Spatial distribution goodness-of-fit test
berman.test
Berman's goodness-of-fit tests
envelope
critical envelope for Monte Carlo test of goodness-of-fit
scan.test
spatial scan statistic/test
dclf.test
Diggle-Cressie-Loosmore-Ford test
mad.test
Mean Absolute Deviation test
dclf.progress
Progress plot for DCLF test
mad.progress
Progress plot for MAD test
Sensitivity diagnostics: Classical measures of model sensitivity such as leverage and influence have been adapted to point process models.
leverage.ppm
Leverage for point process model
influence.ppm
Influence for point process model
dfbetas.ppm
Parameter influence
Diagnostics for covariate effect: Classical diagnostics for covariate effects have been adapted to point process models.
parres
Partial residual plot
addvar
Added variable plot
rhohat
Kernel estimate of covariate effect
Residual diagnostics: Residuals for a fitted point process model, and diagnostic plots based on the residuals, were introduced in Baddeley et al (2005) and Baddeley, Rubak and Moller (2011). Type demo(diagnose) for a demonstration of the diagnostics features.
diagnose.ppm
diagnostic plots for spatial trend
qqplot.ppm
diagnostic Q-Q plot for interpoint interaction
residualspaper
examples from Baddeley et al (2005)
Kcom
model compensator of $K$ function
Gcom
model compensator of $G$ function
Kres
score residual of $K$ function
Gres
score residual of $G$ function
psst
pseudoscore residual of summary function
psstA
pseudoscore residual of empty space function
psstG
pseudoscore residual of $G$ function
Resampling and randomisation procedures You can build your own tests based on randomisation and resampling using the following capabilities:
quadratresample
block resampling
rjitter
apply random displacements to points in a pattern
rshift
random shifting of (subsets of) points

IX. DOCUMENTATION

The online manual entries are quite detailed and should be consulted first for information about a particular function. The book Baddeley, Rubak and Turner (2015) is a complete course on analysing spatial point patterns, with full details about spatstat. Older material (which is now out-of-date but is freely available) includes Baddeley and Turner (2005a), a brief overview of the package in its early development; Baddeley and Turner (2005b), a more detailed explanation of how to fit point process models to data; and Baddeley (2010), a complete set of notes from a 2-day workshop on the use of spatstat. Type citation("spatstat") to get a list of these references.

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

Kasper Klitgaard Berthelsen, Ottmar Cronie, Ute Hahn, Abdollah Jalilian, Marie-Colette van Lieshout, Tuomas Rajala, Dominic Schuhmacher and Rasmus Waagepetersen made substantial contributions of code. Additional contributions by Monsuru Adepeju, Corey Anderson, Ang Qi Wei, Sandro Azaele, Malissa Baddeley, Colin Beale, Melanie Bell, Thomas Bendtsen, Ricardo Bernhardt, Andrew Bevan, Brad Biggerstaff, Anders Bilgrau, Leanne Bischof, Christophe Biscio, Roger Bivand, Jose M. Blanco Moreno, Florent Bonneu, Julian Burgos, Simon Byers, Ya-Mei Chang, Jianbao Chen, Igor Chernayavsky, Y.C. Chin, Bjarke Christensen, Jean-Francois Coeurjolly, Robin Corria Ainslie, Marcelino de la Cruz, Peter Dalgaard, Mario D'Antuono, Sourav Das, Peter Diggle, Patrick Donnelly, Ian Dryden, Stephen Eglen, Ahmed El-Gabbas, Belarmain Fandohan, Olivier Flores, David Ford, Peter Forbes, Shane Frank, Janet Franklin, Funwi-Gabga Neba, Oscar Garcia, Agnes Gault, Jonas Geldmann, Marc Genton, Shaaban Ghalandarayeshi, Julian Gilbey, Jason Goldstick, Pavel Grabarnik, C. Graf, Ute Hahn, Andrew Hardegen, Martin Bogsted Hansen, Martin Hazelton, Juha Heikkinen, Mandy Hering, Markus Herrmann, Paul Hewson, Kassel Hingee, Kurt Hornik, Philipp Hunziker, Jack Hywood, Ross Ihaka, Aruna Jammalamadaka, Robert John-Chandran, Devin Johnson, Mahdieh Khanmohammadi, Bob Klaver, Peter Kovesi, Mike Kuhn, Jeff Laake, Frederic Lavancier, Tom Lawrence, Robert Lamb, Jonathan Lee, George Leser, Li Haitao, George Limitsios, Andrew Lister, Ben Madin, Martin Maechler, Kiran Marchikanti, Jeff Marcus, Robert Mark, Peter McCullagh, Monia Mahling, Jorge Mateu Mahiques, Ulf Mehlig, Sebastian Wastl Meyer, Mi Xiangcheng, Lore De Middeleer, Robin Milne, Enrique Miranda, Jesper Moller, Virginia Morera Pujol, Erika Mudrak, Gopalan Nair, Nicoletta Nava, Linda Stougaard Nielsen, Felipe Nunes, Jens Randel Nyengaard, Jens Oehlschlaegel, Thierry Onkelinx, Sean O'Riordan, Evgeni Parilov, Jeff Picka, Nicolas Picard, Mike Porter, Sergiy Protsiv, Adrian Raftery, Suman Rakshit, Ben Ramage, Pablo Ramon, Xavier Raynaud, Matt Reiter, Ian Renner, Tom Richardson, Brian Ripley, Ted Rosenbaum, Barry Rowlingson, Jason Rudokas, John Rudge, Christopher Ryan, Farzaneh Safavimanesh, Aila Sarkka, Cody Schank, Katja Schladitz, Sebastian Schutte, Bryan Scott, Olivia Semboli, Francois Semecurbe, Vadim Shcherbakov, Shen Guochun, Shi Peijian, Harold-Jeffrey Ship, Ida-Maria Sintorn, Yong Song, Malte Spiess, Mark Stevenson, Kaspar Stucki, Michael Sumner, P. Surovy, Ben Taylor, Thordis Linda Thorarinsdottir, Berwin Turlach, Torben Tvedebrink, Kevin Ummer, Medha Uppala, Andrew van Burgel, Tobias Verbeke, Mikko Vihtakari, Alexendre Villers, Fabrice Vinatier, Sasha Voss, Sven Wagner, Hao Wang, H. Wendrock, Jan Wild, Carl G. Witthoft, Selene Wong, Maxime Woringer, Mike Zamboni and Achim Zeileis.

Details

spatstat is a package for the statistical analysis of spatial data. Its main focus is the analysis of spatial patterns of points in two-dimensional space. The points may carry auxiliary data (`marks'), and the spatial region in which the points were recorded may have arbitrary shape.

The package is designed to support a complete statistical analysis of spatial data. It supports

  • creation, manipulation and plotting of point patterns;
  • exploratory data analysis;
  • spatial random sampling;
  • simulation of point process models;
  • parametric model-fitting;
  • non-parametric smoothing and regression;
  • formal inference (hypothesis tests, confidence intervals);
  • model diagnostics.

Apart from two-dimensional point patterns and point processes, spatstat also supports point patterns in three dimensions, point patterns in multidimensional space-time, point patterns on a linear network, patterns of line segments in two dimensions, and spatial tessellations and random sets in two dimensions.

The package can fit several types of point process models to a point pattern dataset:

  • Poisson point process models (by Berman-Turner approximate maximum likelihood or by spatial logistic regression)
  • Gibbs/Markov point process models (by Baddeley-Turner approximate maximum pseudolikelihood, Coeurjolly-Rubak logistic likelihood, or Huang-Ogata approximate maximum likelihood)
  • Cox/cluster point process models (by Waagepetersen's two-step fitting procedure and minimum contrast, composite likelihood, or Palm likelihood)
  • determinantal point process models (by Waagepetersen's two-step fitting procedure and minimum contrast, composite likelihood, or Palm likelihood)

The models may include spatial trend, dependence on covariates, and complicated interpoint interactions. Models are specified by a formula in the R language, and are fitted using a function analogous to lm and glm. Fitted models can be printed, plotted, predicted, simulated and so on.

References

Baddeley, A. (2010) Analysing spatial point patterns in R. Workshop notes. Version 4.1. CSIRO online technical publication. https://research.csiro.au/software/r-workshop-notes/

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press. Baddeley, A. and Turner, R. (2005a) Spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software 12:6, 1--42. URL: www.jstatsoft.org, ISSN: 1548-7660.

Baddeley, A. and Turner, R. (2005b) Modelling spatial point patterns in R. In: A. Baddeley, P. Gregori, J. Mateu, R. Stoica, and D. Stoyan, editors, Case Studies in Spatial Point Pattern Modelling, Lecture Notes in Statistics number 185. Pages 23--74. Springer-Verlag, New York, 2006. ISBN: 0-387-28311-0.

Baddeley, A., Turner, R., Moller, J. and Hazelton, M. (2005) Residual analysis for spatial point processes. Journal of the Royal Statistical Society, Series B 67, 617--666.

Baddeley, A., Rubak, E. and Moller, J. (2011) Score, pseudo-score and residual diagnostics for spatial point process models. Statistical Science 26, 613--646.

Baddeley, A., Turner, R., Mateu, J. and Bevan, A. (2013) Hybrids of Gibbs point process models and their implementation. Journal of Statistical Software 55:11, 1--43. http://www.jstatsoft.org/v55/i11/

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

Diggle, P.J. (2014) Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third edition. Chapman and Hall/CRC.

Gelfand, A.E., Diggle, P.J., Fuentes, M. and Guttorp, P., editors (2010) Handbook of Spatial Statistics. CRC Press.

Huang, F. and Ogata, Y. (1999) Improvements of the maximum pseudo-likelihood estimators in various spatial statistical models. Journal of Computational and Graphical Statistics 8, 510--530.

Illian, J., Penttinen, A., Stoyan, H. and Stoyan, D. (2008) Statistical Analysis and Modelling of Spatial Point Patterns. Wiley. Waagepetersen, R. An estimating function approach to inference for inhomogeneous Neyman-Scott processes. Biometrics 63 (2007) 252--258.