Analysing spatial point patterns in R - CSIRO

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34 Objects, classes and methods in R > data(humberside) > plot(humberside) humberside Exercise 1 Find out how to modify the command plot(swedishpines) so that the title reads “Swedish Pines data” and the points are represented by plus-signs instead of circles. When you type print(swedishpines) or just swedishpines, this invokes the generic commandprint, which dispatches to the methodprint.ppp, which prints some sensible information about the point pattern swedishpines at the terminal. > swedishpines planar point pattern: 71 points window: rectangle = [0, 96] x [0, 100] units (one unit = 0.1 metres) The generic command summary is meant to provide basic summary statistics for a dataset. When you type summary(swedishpines) this is dispatched to the method summary.ppp, which computes a sensible set of summary statistics for a point pattern, and prints them at the terminal. > summary(swedishpines) Planar point pattern: 71 points Average intensity 0.0074 points per square unit (one unit = 0.1 metres) Window: rectangle = [0, 96]x[0, 100]units Window area = 9600 square units Unit of length: 0.1 metres The command density is also generic. It is normally used to compute a kernel density estimate of a probability distribution from a vector of numbers. (This “default method” is called density.default.) But there is also a method for point patterns, so that when you type density(swedishpines), this is dispatched to density.ppp which computes a two-dimensional kernel estimate of the intensity function. > plot(density(swedishpines, sigma = 10)) CopyrightCSIRO 2010
5.3 Return values 35 density(swedishpines, sigma = 10) 0.002 0.004 0.006 0.008 0.01 0.012 0.014 To see a list of all methods available in R for a particular generic function such as plot: > methods(plot) To see a list of all methods that are available for a particular class such as ppp: > methods(class = "ppp") [1] affine.ppp as.data.frame.ppp as.im.ppp as.owin.ppp [5] as.ppp.ppp bermantest.ppp by.ppp closing.ppp [9] coords
Page 1 and 2: Analysing spatial point patterns in
Page 3 and 4: CONTENTS 3 Contents PART I. OVERVIE
Page 5 and 6: CONTENTS 5 PART I. OVERVIEW The fir
Page 7 and 8: 130 1.1 Types of data 7 The mark co
Page 9 and 10: 1.2 Typical scientific questions 9
Page 11 and 12: 1.2 Typical scientific questions 11
Page 13 and 14: 13 We’ll cover both classical and
Page 15 and 16: 2.4 Marks and covariates 15 Data ar
Page 17 and 18: 2.4 Marks and covariates 17 example
Page 19 and 20: 3.3 Contributed libraries for R 19
Page 21 and 22: 4.4 Licence 21 The response will be
Page 23 and 24: 0.005 4.6 Exploratory data analysis
Page 25 and 26: 4.7 Models 25 E K(r) 0 500 1000 150
Page 27 and 28: 4.8 Multitype point patterns 27 4.8
Page 29 and 30: 4.8 Multitype point patterns 29 e.g
Page 31 and 32: 4.9 Installed datasets 31 PART II.
Page 33: 5.2 Classes in spatstat 33 Point pa
Page 37 and 38: 5.3 Return values 37 Many of the fu
Page 39 and 40: 6.2 Creating a ppp object 39 To rea
Page 41 and 42: 6.4 Categorical marks 41 longleaf T
Page 43 and 44: 6.6 Checking data 43 > par(mfrow =
Page 45 and 46: 45 7 Converting from GIS formats Th
Page 47 and 48: 8.1 Making windows by hand 47 8.1.3
Page 49 and 50: 8.2 Converting from GIS formats 49
Page 51 and 52: 8.5 Creating a point pattern in any
Page 53 and 54: 53 9 Manipulating point patterns Be
Page 55 and 56: 9.2 Operations on ppp objects 55 [1
Page 57 and 58: 9.2 Operations on ppp objects 57 ma
Page 59 and 60: 9.3 Example 59 You may also notice
Page 61 and 62: 9.5 List of operations on point pat
Page 63 and 64: 63 10 Pixel images in spatstat An o
Page 65 and 66: 10.2 Inspecting an image 65 > f w
Page 67 and 68: 10.2 Inspecting an image 67 > plot(
Page 69 and 70: 10.3 Manipulating images 69 0 200 6
Page 71 and 72: 71 > W V 3) > U 3, 42, Z)) Other
Page 73 and 74: 11.3 Operations involving a tessell
Page 79 and 80: 12.2 Inhomogeneous intensity 79 12.
Page 81 and 82: 12.2 Inhomogeneous intensity 81 den
Page 83 and 84: 13.3 Relative distribution estimate
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1 1 2 4 4 1 2 13.4 Distance map 85
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13.4 Distance map 87 PART IV. POISS
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14.2 Quadrat counting tests for CSR
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14.4 Kolmogorov-Smirnov test of CSR
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14.5 Using covariate data 93 Becaus
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95 15 Maximum likelihood for Poisso
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15.3 Fitting Poisson processes in s
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15.4 Fitted models 99 > ppm(bei, ~s
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15.4 Fitted models 101 > predict(fi
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15.4 Fitted models 103 effectfun(fi
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15.5 Simulating the fitted model 10
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16.2 Validation using residuals 107
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113 PART V. INTERACTION Part V of t
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115 independent + + + + + + + + + +
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19.2 Empty space distances 117 Anot
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19.2 Empty space distances 119 cell
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19.2 Empty space distances 121 Fest
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19.3 Nearest neighbour distances 12
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19.4 Pairwise distances and the K f
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19.4 Pairwise distances and the K f
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19.6 Manipulating and plotting summ
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19.7 Caveats 131 Kest(X) X K(r) 0.0
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20.1 Envelopes and Monte Carlo test
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139 21 Spatial bootstrap methods Sp
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22.2 Cox processes 141 22.2 Cox pro
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22.4 Sequential models 143 rSSI(0.0
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23.1 Fitting a cluster process 145
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23.4 Generic algorithm for minimum
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149 In data sharpening [27] the poi
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25.2 Inhomogeneous cluster models 1
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25.4 Local scaling 153 > data(bei)
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25.4 Local scaling 155 PART VI. GIB
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26.3 Pairwise interaction models 15
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26.4 Higher-order interactions 159
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26.6 Simulating Gibbs models 161 St
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27.2 Fitting Gibbs models in spatst
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27.3 Interpoint interactions 165 27
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27.4 Fitted point process models 16
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27.6 Dealing with nuisance paramete
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171 Stationary Strauss process Firs
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28.2 Residuals for Gibbs processes
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28.2 Residuals for Gibbs processes
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28.3 New methods 177 PART VII. MARK
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29.3 Methodological issues 179 A ma
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181 Chorley−Ribble Data For furth
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30.2 Inspecting a marked point patt
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30.3 Manipulating data 185 > data(l
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187 31 Exploratory tools for multit
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31.2 Simple summaries of neighbouri
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31.3 Distance methods and summary f
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31.4 Randomisation tests 197 31.4 R
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31.4 Randomisation tests 199 > plot
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32.1 Numeric marks: distribution an
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32.3 Reverse conditional moments 20
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33.2 Simulation 205 33.2 Simulation
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33.3 Fitting Poisson models 207 33.
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33.3 Fitting Poisson models 209 whe
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34.1 Gibbs models 211 34.1.3 Pairwi
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34.3 Fitting Gibbs models to multit
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34.3 Fitting Gibbs models to multit
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217 There are also the usual method
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219 lty col key label meaning iso 1
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221 38 Replicated data and hyperfra
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223 H H(r) 0.0 0.2 0.4 0.6 0.8 km h
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REFERENCES 225 References [1] F.P.
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REFERENCES 227 [32] P.J. Diggle. Bi
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Index analysis of deviance, 103 are
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INDEX 231 models, 25, 224 Monte Car
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Analysing spatial point patterns in R - CSIRO

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