spatstat-package: The Spatstat Package

Description Details Getting Started Updates FUNCTIONS AND DATASETS 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 PROCESS MODELS) VI. MODEL FITTING (SPATIAL LOGISTIC REGRESSION) VII. SIMULATION VIII. TESTS AND DIAGNOSTICS IX. DOCUMENTATION Licence Acknowledgements Author(s) References

Description

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

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

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:

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.

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

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
IX. Documentation

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
lpp point pattern on a linear network

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
marks<-, %mark% attach/reassign marks to a point pattern

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
rpoisppOnLines generate Poisson 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
quadratresample block resampling

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 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
waterstriders Insects on water surface

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
as.im.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
clickbox interactively draw a rectangle

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
as.data.frame.owin convert window to data frame

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
as.polygonal convert pixel mask to polygonal window

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
clickdist measure distance between two points clicked by user

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
rnoise random pixel noise

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
rlinegrid generate a random array of parallel lines through 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
bdist.tiles boundary distance for 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
eroded.volumes volumes of erosions 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
eroded.volumes.boxx volumes of erosions 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
pixellate.linnet approximate by pixel image

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

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
tail.hyperframe last 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
[.layered extract subset of 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
beachcolourmap one special colour map

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
View(X) spreadsheet-style viewer

Classical exploratory tools:

clarkevans Clark and Evans aggregation index
fryplot Fry plot
miplot Morisita Index 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
bw.stoyan Stoyan's rule of thumb for bandwidth for pcf

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
roc Receiver operating characteristic curve

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
lohboot bootstrap 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
rknn theoretical distribution of nearest neighbour distance

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
pcfcross.inhom,pcfdot.inhom inhomogeneous counterparts of pcfcross, pcfdot

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
nnvario nearest neighbour mark variance index

For marks of any type, there are the following:

Gmulti multitype nearest neighbour distribution
Kmulti multitype K-function
Jmulti multitype J-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
pppdist find the optimal match between two point patterns

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

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. 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
pcf3est pair correlation 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
nncross.pp3 find nearest neighbours in another pattern

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
nnwhich.ppx find nearest neighbours

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
Jfox Foxall J-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
pcfmodel.kppm Pair correlation 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
by the method of minimum contrast

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
conditional intensity loglinear in x

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
project.ppm Ensure 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
lambda(x,y) = exp(alpha + beta * Z(x,y))

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
Triplets() Geyer triplets 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
quad create an object of class "quad"

To inspect a quadrature scheme:

plot(Q) plot quadrature scheme Q
print(Q) print basic information about quadrature scheme Q
summary(Q) summary of 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
corners dummy points at corners of the window

To compute weights:

gridweights quadrature weights by the grid-counting rule
dirichletWeights quadrature weights are Dirichlet tile areas

Simulation and goodness-of-fit for fitted models:

rmh.ppm simulate realisations of a fitted model
simulate.ppm simulate realisations of a fitted model
envelope compute simulation envelopes for 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
methods.linfun conversion facilities

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
intensity loglinear in covariate Z

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
simulate.slrm Simulate model

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
rpoisppOnLines generate Poisson 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
rthin random thinning

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
rMosaicField generate random pixel image by assigning random values in each tile 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
segregation.test test of segregation of types

VIII. TESTS AND DIAGNOSTICS

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
anova.ppm Analysis of Deviance for point process models

More recently-developed tests:

dg.test Dao-Genton test
bits.test Balanced independent two-stage 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
rho2hat Kernel estimate of covariate effect (bivariate)

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
compareFit compare compensators of several fitted models

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
rthin random thinning

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, Yongtao Guan, Ute Hahn, Abdollah Jalilian, Marie-Colette van Lieshout, Greg McSwiggan, Tuomas Rajala, Suman Rakshit, Dominic Schuhmacher, Rasmus Waagepetersen and Hangsheng Wang made substantial contributions of code.

Additional contributions and suggestions from Monsuru Adepeju, Corey Anderson, Ang Qi Wei, Jens Astrom, Marcel Austenfeld, Sandro Azaele, Malissa Baddeley, Guy Bayegnak, 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, Kim Colyvas, Rochelle Constantine, Robin Corria Ainslie, Richard Cotton, Marcelino de la Cruz, Peter Dalgaard, Mario D'Antuono, Sourav Das, Tilman Davies, 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, Cenk Icos, Aruna Jammalamadaka, Robert John-Chandran, Devin Johnson, Mahdieh Khanmohammadi, Bob Klaver, Lily Kozmian-Ledward, Peter Kovesi, Mike Kuhn, Jeff Laake, Frederic Lavancier, Tom Lawrence, Robert Lamb, Jonathan Lee, George Leser, Angela Li, 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, Frederico Mestre, Sebastian Wastl Meyer, Mi Xiangcheng, Lore De Middeleer, Robin Milne, Enrique Miranda, Jesper Moller, Ines Moncada, Mehdi Moradi, Virginia Morera Pujol, Erika Mudrak, Gopalan Nair, Nader Najari, 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, Nicholas Read, 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, Tammy L Silva, Ida-Maria Sintorn, Yong Song, Malte Spiess, Mark Stevenson, Kaspar Stucki, Michael Sumner, P. Surovy, Ben Taylor, Thordis Linda Thorarinsdottir, Leigh Torres, 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.

Author(s)

\spatstatAuthors

.

References

Baddeley, A. (2010) Analysing spatial point patterns in R. Workshop notes, Version 4.1. Online technical publication, CSIRO. https://research.csiro.au/software/wp-content/uploads/sites/6/2015/02/Rspatialcourse_CMIS_PDF-Standard.pdf

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.


spatstat documentation built on April 5, 2018, 5:04 p.m.