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
This is a summary of the features of spatstat, a package in R for the statistical analysis of spatial point patterns.
spatstat is a package for the statistical analysis of spatial data. Its main focus is the analysis of spatial patterns of points in twodimensional 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 modelfitting;
nonparametric smoothing and regression;
formal inference (hypothesis tests, confidence intervals);
model diagnostics.
Apart from twodimensional point patterns and point processes, spatstat also supports point patterns in three dimensions, point patterns in multidimensional spacetime, 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 BermanTurner approximate maximum likelihood or by spatial logistic regression)
Gibbs/Markov point process models (by BaddeleyTurner approximate maximum pseudolikelihood, CoeurjollyRubak logistic likelihood, or HuangOgata approximate maximum likelihood)
Cox/cluster point process models (by Waagepetersen's twostep fitting procedure and minimum contrast, composite likelihood, or Palm likelihood)
determinantal point process models (by Waagepetersen's twostep 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.
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.rproject.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')
.
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.
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.
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 
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  threedimensional 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 Strausshard core process (perfect simulation) 
rDiggleGratton  simulate DiggleGratton process (perfect simulation) 
rDGS  simulate DiggleGatesStibbard process (perfect simulation) 
rPenttinen  simulate Penttinen process (perfect simulation) 
rNeymanScott  simulate a general NeymanScott process 
rPoissonCluster  simulate a general Poisson cluster process 
rMatClust  simulate the Matern Cluster process 
rThomas  simulate the Thomas process 
rGaussPoisson  simulate the GaussPoisson cluster process 
rCauchy  simulate NeymanScott Cauchy cluster process 
rVarGamma  simulate NeymanScott Variance Gamma cluster process 
rthin  random thinning 
rcell  simulate the BaddeleySilverman cell process 
rmh  simulate Gibbs point process using MetropolisHastings 
simulate.ppm  simulate Gibbs point process using MetropolisHastings 
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 lazyloaded, 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  UptonFingleton sea anemones data 
ants  HarknessIsham 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  CrickRipley biological cells data 
chicago  Chicago crimes 
chorley  ChorleyRibble cancer data 
clmfires  CastillaLa Mancha forest fires 
copper  BermanHuntington 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  MarkEslerRipley trees data 
osteo  Osteocyte lacunae (3D, replicated) 
paracou  Kimboto trees in Paracou, French Guiana 
ponderosa  GetisFranklin ponderosa pine trees data 
pyramidal  Pyramidal neurons from 31 brains 
redwood  StraussRipley 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  StrandRipley 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 subpatterns of a point pattern 
cut.ppp  classify the points in a point pattern 
split.ppp  divide pattern into subpatterns 
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 DirichletVoronoi 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  RipleyRasson 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 colourvalued pixel image 
hsvim  create colourvalued 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 DirichletVoronoi 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 
Threedimensional point patterns
An object of class "pp3"
represents a threedimensional
point pattern in a rectangular box. The box is represented by
an object of class "box3"
.
pp3  create a 3D point pattern 
plot.pp3  plot a 3D point pattern 
coords  extract coordinates 
as.hyperframe  extract coordinates 
subset.pp3  extract subset of 3D point pattern 
unitname.pp3  name of unit of length 
npoints  count the number of points 
runifpoint3  generate uniform random points in 3D 
rpoispp3  generate Poisson random points in 3D 
envelope.pp3  generate simulation envelopes for 3D pattern 
box3  create a 3D rectangular box 
as.box3  convert data to 3D 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 
Multidimensional spacetime point patterns
An object of class "ppx"
represents a
point pattern in multidimensional space and/or time.
ppx  create a multidimensional spacetime 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 
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)  spreadsheetstyle 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  crossvalidated bandwidth selection
for density.ppp 
bw.ppl  likelihood crossvalidated bandwidth selection
for density.ppp 
bw.scott  Scott's rule of thumb for density estimation 
bw.relrisk  crossvalidated bandwidth selection
for relrisk 
bw.smoothppp  crossvalidated 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  AllardFraley feature detection 
nnclean  ByersRaftery feature detection 
sharpen.ppp  ChoiHall 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  Jfunction J = (1G)/(1F) 
Kest  Ripley's Kfunction 
Lest  Besag Lfunction 
Tstat  Third order Tfunction 
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  GetisFranklin neighbourhood density function 
localK  neighbourhood Kfunction 
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 Kfunction 
Kscaled  locally scaled Kfunction 
Kest.fft  fast Kfunction 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 Kfunctions K[i,j], K[i.] 
Lcross,Ldot  multitype Lfunctions L[i,j], L[i.] 
Jcross,Jdot,Jmulti  multitype Jfunctions 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 Ifunction 
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 crosscorrelation function 
markvario  mark variogram 
Kmark  markweighted 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 Kfunction 
Jmulti  multitype Jfunction 
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 threedimensional point pattern:
These are for 3dimensional point pattern objects (class pp3
).
F3est  empty space function F 
G3est  nearest neighbour function G 
K3est  Kfunction 
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 multidimensional point pattern:
These are for multidimensional spacetime
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 Gfunction 
Jfox  Foxall Jfunction 
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  Variancecovariance 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
.
Lowerlevel fitting functions include:
lgcp.estK  fit a logGaussian Cox process model 
lgcp.estpcf  fit a logGaussian 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 NeymanScott Cauchy cluster process 
cauchy.estpcf  fit a NeymanScott Cauchy cluster process 
vargamma.estK  fit a NeymanScott Variance Gamma process 
vargamma.estpcf  fit a NeymanScott Variance Gamma process 
mincontrast  lowlevel algorithm for fitting models 
by the method of minimum contrast 
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 nonuniform 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  Variancecovariance 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  loglikelihood or logpseudolikelihood 
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)  Logcubic polynomial trend 
X ~ harmonic(x,y,2)  Logharmonic 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()  Areainteraction process 
BadGey()  multiscale Geyer process 
Concom()  connected component interaction 
DiggleGratton()  DiggleGratton potential 
DiggleGatesStibbard()  DiggleGatesStibbard 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 Strausshard core process 
Hybrid()  Hybrid of several interactions 
LennardJones()  LennardJones potential 
MultiHard()  multitype hard core process 
MultiStrauss()  multitype Strauss process 
MultiStraussHard()  multitype Strauss/hard core process 
OrdThresh()  Ord process, threshold potential 
Ord()  Ord model, usersupplied potential 
PairPiece()  pairwise interaction, piecewise constant 
Pairwise()  pairwise interaction, usersupplied potential 
Penttinen()  Penttinen pairwise interaction 
SatPiece()  Saturated pair model, piecewise constant potential 
Saturated()  Saturated pair model, usersupplied 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 gridcounting rule 
dirichletWeights  quadrature weights are Dirichlet tile areas 
Simulation and goodnessoffit 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 
Code for fitting determinantal point process models has recently been added to spatstat.
For information, see the help file for dppm
.
Logistic regression
Pixelbased 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 pixelbased 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  Variancecovariance 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
.
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 Strausshard core process (perfect simulation) 
rDiggleGratton  simulate DiggleGratton process (perfect simulation) 
rDGS  simulate DiggleGatesStibbard process (perfect simulation) 
rPenttinen  simulate Penttinen process (perfect simulation) 
rNeymanScott  simulate a general NeymanScott process 
rMatClust  simulate the Matern Cluster process 
rThomas  simulate the Thomas process 
rLGCP  simulate the logGaussian Cox process 
rGaussPoisson  simulate the GaussPoisson cluster process 
rCauchy  simulate NeymanScott process with Cauchy clusters 
rVarGamma  simulate NeymanScott process with Variance Gamma clusters 
rcell  simulate the BaddeleySilverman 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 
Simulationbased inference
envelope  critical envelope for Monte Carlo test of goodnessoffit 
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 
Hypothesis tests:
quadrat.test  chi^2 goodnessoffit test on quadrat counts 
clarkevans.test  Clark and Evans test 
cdf.test  Spatial distribution goodnessoffit test 
berman.test  Berman's goodnessoffit tests 
envelope  critical envelope for Monte Carlo test of goodnessoffit 
scan.test  spatial scan statistic/test 
dclf.test  DiggleCressieLoosmoreFord test 
mad.test  Mean Absolute Deviation test 
anova.ppm  Analysis of Deviance for point process models 
More recentlydeveloped tests:
dg.test  DaoGenton test 
bits.test  Balanced independent twostage 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 QQ 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 
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 outofdate 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 2day workshop on the use of spatstat.
Type citation("spatstat")
to get a list of these references.
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.
Kasper Klitgaard Berthelsen, Ottmar Cronie, Yongtao Guan, Ute Hahn, Abdollah Jalilian, MarieColette 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, YaMei Chang, Jianbao Chen, Igor Chernayavsky, Y.C. Chin, Bjarke Christensen, JeanFrancois 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 ElGabbas, Belarmain Fandohan, Olivier Flores, David Ford, Peter Forbes, Shane Frank, Janet Franklin, FunwiGabga 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 JohnChandran, Devin Johnson, Mahdieh Khanmohammadi, Bob Klaver, Lily KozmianLedward, 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, HaroldJeffrey Ship, Tammy L Silva, IdaMaria 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.
.
Baddeley, A. (2010) Analysing spatial point patterns in R. Workshop notes, Version 4.1. Online technical publication, CSIRO. https://research.csiro.au/software/wpcontent/uploads/sites/6/2015/02/Rspatialcourse_CMIS_PDFStandard.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: 15487660.
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. SpringerVerlag, New York, 2006. ISBN: 0387283110.
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, pseudoscore 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 SpatioTemporal 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 pseudolikelihood 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 NeymanScott processes. Biometrics 63 (2007) 252–258.
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