Analysing spatial point patterns in R - CSIRO

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84 Dependence of intensity on a covariate > plot(rhohat(bei, slope)) rhohat(bei, slope) ρ(slope) 0.005 0.010 0.015 rho hi lo 0.00 0.05 0.10 0.15 0.20 0.25 0.30 slope The plot is an estimate of the intensity ρ(z) as a function of terrain slope z. It indicates that the Beilschmiedia trees are relatively unlikely to be found on flat terrain (where the slope is less than 0.05) compared to steeper slopes. Additional capabilities will be added into spatstat in the near future. 13.4 Distance map The dataset copper gives the locations of copper deposits in a survey region, and also the location of geological lineaments (which are mostly geological faults). It is conjectured that copper is more likely to be deposited close to a fault. > data(copper) > X L plot(X, pch = 16, main = "copper data") > plot(L, add = TRUE) copper data CopyrightCSIRO 2010
1 1 2 4 4 1 2 13.4 Distance map 85 To apply the methods described above, the covariate information contained in the map of geological faults L must be converted into a covariate that is a function Z(u) of spatial location u. A natural choice is the distance function Z(u) = distance from u to L This can be computed by the command distmap, which returns a pixel image containing the values Z(u) at a fine grid of pixels u. > Z plot(L, lwd = 2, main = "") > contour(Z, add = TRUE) 1 9 3 6 5 2 2 4 3 3 1 4 1 2 2 1 2 1 1 1 4 1 1 3 2 3 1 3 2 3 1 5 4 2 2 1 4 1 3 2 5 2 1 3 4 1 2 1 1 3 1 1 1 1 3 1 2 1 1 3 1 1 1 2 1 1 2 3 2 1 2 4 1 3 3 3 2 2 1 3 5 6 4 3 1 2 2 5 2 1 1 4 3 4 1 2 3 2 3 5 4 4 1 1 3 1 1 4 1 2 2 1 1 4 1 1 1 2 1 3 1 1 1 1 1 2 1 2 4 5 1 1 1 1 3 1 Having created this covariate image we can now apply the other techniques such as relative distributions. > plot(rhohat(X, Z), xlab = "Distance to nearest fault") rhohat(X, Z) ρ(Z) 0.000 0.005 0.010 0.015 0.020 0.025 rho hi lo 0 1 2 3 4 5 Distance to nearest fault CopyrightCSIRO 2010
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Analysing spatial point patterns in
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CONTENTS 3 Contents PART I. OVERVIE
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CONTENTS 5 PART I. OVERVIEW The fir
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130 1.1 Types of data 7 The mark co
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1.2 Typical scientific questions 9
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1.2 Typical scientific questions 11
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13 We’ll cover both classical and
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2.4 Marks and covariates 15 Data ar
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2.4 Marks and covariates 17 example
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3.3 Contributed libraries for R 19
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4.4 Licence 21 The response will be
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0.005 4.6 Exploratory data analysis
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4.7 Models 25 E K(r) 0 500 1000 150
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4.8 Multitype point patterns 27 4.8
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4.8 Multitype point patterns 29 e.g
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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
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: 13.3 Relative distribution estimate
Page 87 and 88: 13.4 Distance map 87 PART IV. POISS
Page 89 and 90: 14.2 Quadrat counting tests for CSR
Page 91 and 92: 14.4 Kolmogorov-Smirnov test of CSR
Page 93 and 94: 14.5 Using covariate data 93 Becaus
Page 95 and 96: 95 15 Maximum likelihood for Poisso
Page 97 and 98: 15.3 Fitting Poisson processes in s
Page 99 and 100: 15.4 Fitted models 99 > ppm(bei, ~s
Page 101 and 102: 15.4 Fitted models 101 > predict(fi
Page 103 and 104: 15.4 Fitted models 103 effectfun(fi
Page 105 and 106: 15.5 Simulating the fitted model 10
Page 107 and 108: 16.2 Validation using residuals 107
Page 113 and 114: 113 PART V. INTERACTION Part V of t
Page 115 and 116: 115 independent + + + + + + + + + +
Page 117 and 118: 19.2 Empty space distances 117 Anot
Page 119 and 120: 19.2 Empty space distances 119 cell
Page 121 and 122: 19.2 Empty space distances 121 Fest
Page 123 and 124: 19.3 Nearest neighbour distances 12
Page 125 and 126: 19.4 Pairwise distances and the K f
Page 127 and 128: 19.4 Pairwise distances and the K f
Page 129 and 130: 19.6 Manipulating and plotting summ
Page 131 and 132: 19.7 Caveats 131 Kest(X) X K(r) 0.0
Page 133 and 134: 20.1 Envelopes and Monte Carlo test
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20.1 Envelopes and Monte Carlo test
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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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