Analysing spatial point patterns in R - CSIRO

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220 Point patterns in multi-dimensional space-time Multidimensional point pattern 100 points 1 column of marks: marks Domain: 4-dimensional box: [0, 3] x [0, 3] x [0, 2] x [0, 1] units The window containing the point pattern is currently required to be a rectangular box, stored as an object of class "boxx", created by the function boxx. Facilities available for boxx objects include print, summary, diameter, volume, shortside and eroded.volumes. Facilities currently available for ppx objects include: print print basic information summary print detailed summary of data as.data.frame extract coordinates and marks npoints number of points coords extract coordinates coords
221 38 Replicated data and hyperframes Sometimes the data may consist of several point patterns. We may have replicated point pattern data obtained by repeating an experiment, such as the locations of cell nuclei in 10 different samples of tissue. These data could be stored in a simple list Z, where the ith entry in the list, Z[[i]], is the ith point pattern object. A hyperframe is like a data frame, except that the entries can be any type of object. For example, a hyperframe can include a column, each of whose entries is a point pattern. The only constraint is that all the entries in a column must be of the same type. A hyperframe is a convenient way to store replicated point pattern data together with auxiliary data. A hyperframe can store the results of a designed experiment where the “response” is a point pattern and the covariates are other types of data. The following facilities are available: hyperframe create a hyperframe as.hyperframe convert other data to a hyperframe print.hyperframe print a representation of a hyperframe dim.hyperframe dimensions of hyperframe $.hyperframe extract column of hyperframe [.hyperframe extract subset of hyperframe [ data(osteo) > osteo[1:5, ] Hyperframe: id shortid brick pts depth 1 c77za4 4 1 (pp3) 45 2 c77za4 4 2 (pp3) 60 3 c77za4 4 3 (pp3) 55 4 c77za4 4 4 (pp3) 60 5 c77za4 4 5 (pp3) 85 The command with.hyperframe can be used to evaluate an expression in each row of the hyperframe. For example, to count the number of points in each of the first 10 patterns: > with(osteo, npoints(pts))[1:10] 1 2 3 4 5 6 7 8 9 10 13 11 11 12 14 12 16 15 18 16 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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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
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
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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 and 186: 30.3 Manipulating data 185 > data(l
Page 187 and 188: 187 31 Exploratory tools for multit
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
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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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