Analysing spatial point patterns in R - CSIRO

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10 Introduction Example 4 (Chorley-Ribble data) An apparent cluster of cases of cancer of the larynx occurred near a disused industrial incinerator. The area health authority mapped the domicile locations of all cases (58) of cancer of the larynx and, for control purposes, a random sample of cases (978) of lung cancer. Main question: after allowing for spatial variation in density of the susceptible population (for which the lung cancer cases are a surrogate), is there evidence of raised incidence of laryngeal cancer near the incinerator Chorley−Ribble Data larynx lung incinerator 1.2.4 Segregation of points with different marks In a marked point pattern, we need to investigate whether points with different mark values are ‘segregated’ (found in different parts of the study region). Example 5 (Lansing Woods) In a 20-acre study region in Lansing Woods, Michigan, the locations of 2251 trees and the botanical classification of each tree were recorded. Main question: is the study region divided into domains where a single tree species dominates, or are the different species randomly interspersed CopyrightCSIRO 2010
1.2 Typical scientific questions 11 blackoak + + + ++ + + + + + + + + + + ++ + + ++ + ++ + + +++ +++ + + + + + +++++ + ++ + + + ++ + + + + + + + + + ++ + + + ++ ++ + + ++ + +++ + + + + + + + + + + + + ++ + + + + + + + + + + + + + + + + + + + + + + hickory maple ++ + ++ ++ ++ + ++ ++++ + + ++ +++ + ++ ++ + ++ + + ++ ++ +++ ++ + + + ++ ++ + +++ + + + ++ + ++ + + ++ + + + + + + + + + + + ++ + + +++ + + + + ++ + + + + ++ + ++ + + + + ++ + ++ + + + + ++ + + ++ ++ + + + ++ + + ++ ++ + ++ + + ++ + ++ + ++ + + + ++ + + + + + + ++ + + + + ++ + + +++ + ++ ++ + + + + + + + + ++ ++ ++ + + ++ + + + + + + + + + + + + ++ + + + + + + + +++ + + + + + + + + + + + + ++ + ++ + + ++ + +++ +++ + + + + + ++ ++ + ++ + + + ++ + + + + ++ + ++ + + +++ + ++ + + + ++ + + ++ + + + + + + + + ++ ++ ++ + ++ ++ ++ + ++ + + + ++ ++ + + ++ + ++ +++ + ++ + ++ + + ++ + + + ++ + + + + + + + + + + ++ + + + + +++ + + ++ + + + ++ + + + + + + ++ ++ + + + + ++ + +++ ++ ++ + + + ++ + + + ++ + + ++ ++ + + + + ++ + + + + + ++ + + + ++ + ++ + + + ++ + + + + ++ ++ + + + + + + ++ + + + + + + + + + + + ++ + + ++ ++ +++ + + + + + + + + + + ++ + + + + + + + + + + ++ ++ + + + + + + + ++ + + + + + + + + + + ++ + +++ +++ + + + + + + + + + + + + + ++ + ++ + + + ++ ++++ + + ++ ++ ++ ++ + + + + ++ ++ + + + + + ++ + + + ++ + + + + + ++++ + + + + + + + ++ + ++ + + + + + + + + + + ++ + + + + ++ + + + + + + ++ + + ++ + ++++ + ++ + ++ ++ ++ ++ ++ + + ++ + ++ ++ + + + + + + + + + + + + + + ++ ++++ ++ + + ++++ + + + ++ + + + + + +++ + + +++ + + + + + + + + + ++ ++ ++ + + + + + + + + + + + ++ +++ + + + + + + + ++ + + + + + + + +++ + + Example 6 (Longleaf Pines) In a forest of Longleaf Pine trees in Georgia, USA, the locations of 584 trees were recorded along with their diameter at breast height (dbh), a convenient surrogate measure of size and age. Main question: explain any spatial variation in the density and age of trees. Longleaf Pines 1.2.5 Dependence between points of different types In a point pattern dataset with categorical marks, (aka multitype point pattern), dependence between the different types may be formulated either as interaction between the sub-pattern of points of type i and the sub-pattern of points of type j; or dependence between the mark values of points at two specified locations. Example 7 (Amacrine cells) The retina is a flat sheet containing several layers of cells. Amacrine cells occupy two adjacent layers, the ‘on’ and ‘off’ layers. In a microscope field of view, the locations of all amacrine cells were mapped, and classified into ‘on’ and ‘off’. Main question: is there evidence that the ‘on’ and ‘off’ layers grew independently of one another CopyrightCSIRO 2010
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: 1.2 Typical scientific questions 9
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 and 34: 5.2 Classes in spatstat 33 Point pa
Page 35 and 36: 5.3 Return values 35 density(swedis
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
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9.5 List of operations on point pat
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63 10 Pixel images in spatstat An o
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10.2 Inspecting an image 65 > f w
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10.2 Inspecting an image 67 > plot(
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10.3 Manipulating images 69 0 200 6
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71 > W V 3) > U 3, 42, Z)) Other
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11.3 Operations involving a tessell
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12.2 Inhomogeneous intensity 79 12.
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12.2 Inhomogeneous intensity 81 den
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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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