Analysing spatial point patterns in R - CSIRO

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186 Handling marked point pattern data marked planar point pattern: 584 points marks are numeric, of type double window: rectangle = [0, 200] x [0, 200] metres > X X marked planar point pattern: 584 points multitype, with levels = juvenile adult window: rectangle = [0, 200] x [0, 200] metres > par(mfrow = c(1, 2)) > plot(longleaf) 0 20 40 60 80 0.000000 1.722522 3.445045 5.167567 6.890090 > plot(X, main = "cut(longleaf)") juvenile adult 1 2 > par(mfrow = c(1, 1)) longleaf cut(longleaf) If the marks are a data frame, use the second argument z to specify which column should be used for the cut. For example, to classify New Brunswick fires into three groups by fire size, > data(nbfires) > Y
187 31 Exploratory tools for multitype point patterns This section covers some tools for exploratory data analysis of multitype point patterns (i.e. where the marks are categorical). 31.1 Intensity The Lansing Woods data give the locations of 6 species of trees in a forest in Michigan. Elementary estimates of the frequency distribution of species, and the intensity of each species, are available from summary.ppp. > data(lansing) > summary(lansing) Marked planar point pattern: 2251 points Average intensity 2250 points per square unit (one unit = 924 feet) *Pattern contains duplicated points* Multitype: frequency proportion intensity blackoak 135 0.0600 135 hickory 703 0.3120 703 maple 514 0.2280 514 misc 105 0.0466 105 redoak 346 0.1540 346 whiteoak 448 0.1990 448 Window: rectangle = [0, 1]x[0, 1]units Window area = 1 square unit Unit of length: 924 feet It’s sensible to examine the sub-patterns of different types separately, using split.ppp. > plot(split(lansing)) 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.
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5.2 Classes in spatstat 33 Point pa
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5.3 Return values 35 density(swedis
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5.3 Return values 37 Many of the fu
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6.2 Creating a ppp object 39 To rea
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6.4 Categorical marks 41 longleaf T
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6.6 Checking data 43 > par(mfrow =
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45 7 Converting from GIS formats Th
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8.1 Making windows by hand 47 8.1.3
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8.2 Converting from GIS formats 49
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8.5 Creating a point pattern in any
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53 9 Manipulating point patterns Be
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9.2 Operations on ppp objects 55 [1
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9.2 Operations on ppp objects 57 ma
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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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Page 139 and 140: 139 21 Spatial bootstrap methods Sp
Page 141 and 142: 22.2 Cox processes 141 22.2 Cox pro
Page 143 and 144: 22.4 Sequential models 143 rSSI(0.0
Page 145 and 146: 23.1 Fitting a cluster process 145
Page 147 and 148: 23.4 Generic algorithm for minimum
Page 149 and 150: 149 In data sharpening [27] the poi
Page 151 and 152: 25.2 Inhomogeneous cluster models 1
Page 153 and 154: 25.4 Local scaling 153 > data(bei)
Page 155 and 156: 25.4 Local scaling 155 PART VI. GIB
Page 157 and 158: 26.3 Pairwise interaction models 15
Page 159 and 160: 26.4 Higher-order interactions 159
Page 161 and 162: 26.6 Simulating Gibbs models 161 St
Page 163 and 164: 27.2 Fitting Gibbs models in spatst
Page 165 and 166: 27.3 Interpoint interactions 165 27
Page 167 and 168: 27.4 Fitted point process models 16
Page 169 and 170: 27.6 Dealing with nuisance paramete
Page 171 and 172: 171 Stationary Strauss process Firs
Page 173 and 174: 28.2 Residuals for Gibbs processes
Page 175 and 176: 28.2 Residuals for Gibbs processes
Page 177 and 178: 28.3 New methods 177 PART VII. MARK
Page 179 and 180: 29.3 Methodological issues 179 A ma
Page 181 and 182: 181 Chorley−Ribble Data For furth
Page 183 and 184: 30.2 Inspecting a marked point patt
Page 185: 30.3 Manipulating data 185 > data(l
Page 189 and 190: 31.2 Simple summaries of neighbouri
Page 191 and 192: 31.3 Distance methods and summary f
Page 197 and 198: 31.4 Randomisation tests 197 31.4 R
Page 199 and 200: 31.4 Randomisation tests 199 > plot
Page 201 and 202: 32.1 Numeric marks: distribution an
Page 203 and 204: 32.3 Reverse conditional moments 20
Page 205 and 206: 33.2 Simulation 205 33.2 Simulation
Page 207 and 208: 33.3 Fitting Poisson models 207 33.
Page 209 and 210: 33.3 Fitting Poisson models 209 whe
Page 211 and 212: 34.1 Gibbs models 211 34.1.3 Pairwi
Page 213 and 214: 34.3 Fitting Gibbs models to multit
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Page 217 and 218: 217 There are also the usual method
Page 219 and 220: 219 lty col key label meaning iso 1
Page 221 and 222: 221 38 Replicated data and hyperfra
Page 223 and 224: 223 H H(r) 0.0 0.2 0.4 0.6 0.8 km h
Page 225 and 226: REFERENCES 225 References [1] F.P.
Page 227 and 228: REFERENCES 227 [32] P.J. Diggle. Bi
Page 229 and 230: Index analysis of deviance, 103 are
Page 231 and 232: INDEX 231 models, 25, 224 Monte Car
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Analysing spatial point patterns in R - CSIRO

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