spatstat.explore-package {spatstat.explore}

The spatstat.explore Package

Description

The spatstat.explore package belongs to the spatstat family of packages. It contains the core functionality for statistical analysis and modelling of spatial data.

Details

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

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

This sub-package spatstat.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.)

Structure of the spatstat family

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

• spatstat.utils containing basic utilities

• spatstat.sparse containing linear algebra utilities

• spatstat.data containing datasets

• spatstat.geom containing geometrical objects and geometrical operations

• spatstat.explore containing the 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.

Overview of Functionality in spatstat.explore

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.ppp	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

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, 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.

Author(s)

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