The spatstat.explore package belongs to the spatstat family of packages. It contains the core functionality for statistical analysis and modelling of spatial data.
The orginal spatstat package grew to be very large. It has now been divided into several sub-packages:
spatstat.utils containing basic utilities
spatstat.sparse containing linear algebra utilities
spatstat.data containing datasets
spatstat.geom containing geometrical objects and geometrical operations
spatstat.explore containing the functionality for exploratory data analysis and nonparametric analysis of spatial data.
spatstat.model containing the functionality for statistical modelling, model-fitting, formal statistical inference and informal model diagnostics.
spatstat.linnet containing functions for spatial data on a linear network
spatstat, which simply loads the other sub-packages listed above, and provides documentation.
When you install spatstat, these sub-packages are also
installed. Then if you load the spatstat package by typing
library(spatstat), the other sub-packages listed above will
automatically be loaded or imported.
For an overview of all the functions available in
the sub-packages of spatstat,
see the help file for "spatstat-package"
in the spatstat package.
Additionally there are several extension packages:
spatstat.gui for interactive graphics
spatstat.local for local likelihood (including geographically weighted regression)
spatstat.Knet for additional, computationally efficient code for linear networks
spatstat.sphere (under development) for spatial data on a sphere, including spatial data on the earth's surface
The extension packages must be installed separately and loaded explicitly if needed. They also have separate documentation.
The spatstat family of packages is designed to support a complete statistical analysis of spatial data. It supports
creation, manipulation and plotting of point patterns;
exploratory data analysis;
spatial random sampling;
simulation of point process models;
parametric model-fitting;
non-parametric smoothing and regression;
formal inference (hypothesis tests, confidence intervals);
model diagnostics.
For an overview, see the help file for "spatstat-package"
in the spatstat package.
Following is a list of the functionality provided in the spatstat.explore package only.
To simulate a random point pattern:
Functions for generating random point patterns are now contained in the spatstat.random package.
To interrogate a point pattern:
density.ppp | kernel estimation of point pattern intensity |
densityHeat.ppp | diffusion kernel estimation of point pattern intensity |
Smooth.ppp | kernel smoothing of marks of point pattern |
sharpen.ppp | data sharpening |
Manipulation of pixel images:
An object of class "im" represents a pixel image.
blur | apply Gaussian blur to image |
Smooth.im | apply Gaussian blur to image |
transect.im | line transect of image |
pixelcentres | extract centres of pixels |
rnoise | random pixel noise |
Line segment patterns
An object of class "psp" represents a pattern of straight line
segments.
density.psp | kernel smoothing of line segments |
rpoisline | generate a realisation of the Poisson line process inside a window |
Tessellations
An object of class "tess" represents a tessellation.
rpoislinetess | generate tessellation using Poisson line process |
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".
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 |
Multi-dimensional space-time point patterns
An object of class "ppx" represents a
point pattern in multi-dimensional space and/or time.
runifpointx | generate uniform random points |
rpoisppx | generate Poisson random points |
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.CvL | Cronie-Van Lieshout bandwidth selection for density estimation |
bw.scott | Scott's rule of thumb for density estimation |
bw.abram | Abramson's rule for adaptive bandwidths |
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:
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 |
density.ppp | kernel smoothed density |
densityHeat.ppp | diffusion 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 \(G_{ij}, G_{i\bullet}\) |
Kcross,Kdot, Kmulti | multitype \(K\)-functions \(K_{ij}, K_{i\bullet}\) |
Lcross,Ldot | multitype \(L\)-functions \(L_{ij}, L_{i\bullet}\) |
Jcross,Jdot,Jmulti | multitype \(J\)-functions \(J_{ij}, J_{i\bullet}\) |
pcfcross | multitype pair correlation function \(g_{ij}\) |
pcfdot | multitype pair correlation function \(g_{i\bullet}\) |
pcfmulti | general pair correlation function |
markconnect | marked connection function \(p_{ij}\) |
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 |
localKcross,localKdot | local counterparts of Kcross, Kdot |
localLcross,localLdot | local counterparts of Lcross, Ldot |
localKcross.inhom,localLcross.inhom | local counterparts of Kcross.inhom, Lcross.inhom |
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 |
markmarkscatter | mark-mark scatterplot |
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:
marktable | tabulate the marks of neighbours in a point pattern |
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 |
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 |
Model fitting
Functions for fitting point process models are now contained in the spatstat.model package.
Simulation
There are many ways to generate a random point pattern, line segment pattern, pixel image or tessellation in spatstat.
Random point patterns: Functions for random generation are now contained in the spatstat.random package.
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.
Methods for simulating a fitted model are now contained in the spatstat.model package.
Other random patterns: Functions for random generation are now contained in the spatstat.random package.
Simulation-based inference
envelope | critical envelope for Monte Carlo test of goodness-of-fit |
bits.envelope | critical envelope for balanced two-stage Monte Carlo test |
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 | \(\chi^2\) 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 |
Model diagnostics:
Classical measures of model sensitivity such as leverage and influence, and classical model diagnostic tools such as residuals, partial residuals, and effect estimates, have been adapted to point process models. These capabilities are now provided in the spatstat.model package.
Resampling and randomisation procedures
You can build your own tests based on randomisation and resampling using the following capabilities:
quadratresample | block resampling |
rshift | random shifting of (subsets of) points |
rthin | random thinning |
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.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
Kasper Klitgaard Berthelsen, Ottmar Cronie, Tilman Davies, Julian Gilbey, Yongtao Guan, Ute Hahn, Kassel Hingee, Abdollah Jalilian, Marie-Colette van Lieshout, Greg McSwiggan, Tuomas Rajala, Suman Rakshit, Dominic Schuhmacher, Rasmus Waagepetersen and Hangsheng Wang made substantial contributions of code.
For comments, corrections, bug alerts and suggestions, we thank Monsuru Adepeju, Corey Anderson, Ang Qi Wei, Ryan Arellano, Jens Astrom, Robert Aue, 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, Jordan Brown, Ian Buller, Julian Burgos, Simon Byers, Ya-Mei Chang, Jianbao Chen, Igor Chernayavsky, Y.C. Chin, Bjarke Christensen, Lucia Cobo Sanchez, Jean-Francois Coeurjolly, Kim Colyvas, Hadrien Commenges, Rochelle Constantine, Robin Corria Ainslie, Richard Cotton, Marcelino de la Cruz, Peter Dalgaard, Mario D'Antuono, Sourav Das, Peter Diggle, Patrick Donnelly, Ian Dryden, Stephen Eglen, Ahmed El-Gabbas, Belarmain Fandohan, Olivier Flores, David Ford, Peter Forbes, Shane Frank, Janet Franklin, Funwi-Gabga Neba, Oscar Garcia, Agnes Gault, Jonas Geldmann, Marc Genton, Shaaban Ghalandarayeshi, Jason Goldstick, Pavel Grabarnik, C. Graf, Ute Hahn, Andrew Hardegen, Martin Bogsted Hansen, Martin Hazelton, Juha Heikkinen, Mandy Hering, Markus Herrmann, Maximilian Hesselbarth, Paul Hewson, Hamidreza Heydarian, 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, Robert Lamb, Frederic Lavancier, Tom Lawrence, Tomas Lazauskas, Jonathan Lee, George Leser, Angela Li, Li Haitao, George Limitsios, Andrew Lister, Nestor Luambua, 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, Annie Mollie, 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, Tim Pollington, Mike Porter, Sergiy Protsiv, Adrian Raftery, Ben Ramage, Pablo Ramon, Xavier Raynaud, Nicholas Read, Matt Reiter, Ian Renner, Tom Richardson, Brian Ripley, Ted Rosenbaum, Barry Rowlingson, Jason Rudokas, Tyler Rudolph, 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, Jan Sulavik, 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, Maximilian Vogtland, Sasha Voss, Sven Wagner, Hao Wang, H. Wendrock, Jan Wild, Carl G. Witthoft, Selene Wong, Maxime Woringer, Luke Yates, Mike Zamboni and Achim Zeileis.
spatstat is a family of R packages for the statistical analysis of spatial data. Its main focus is the analysis of spatial patterns of points in two-dimensional space.
The original spatstat package has now been split into several sub-packages.
This sub-package spatstat.explore contains the user-level functions that perform exploratory data analysis and nonparametric data analysis of spatial data.
(The main exception is that functions for linear networks are in the separate sub-package spatstat.linnet.)