Analysing spatial point patterns in R - CSIRO

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62 Manipulating point patterns X print basic info print(X) print basic info summary(X) print detailed summary npoints(X) number of points coords(X) extract coordinates of points coords(X)
63 10 Pixel images in spatstat An object of class "im" represents a pixel image. It specifies a rectangular grid of locations (“pixels”) in two dimensional space, and a numerical value for each pixel. The pixel values can be real numbers, integers, complex numbers, single characters or strings, logical values or categorical values. A pixel’s value can also be NA, meaning that it is not defined at that location. A pixel image represents a spatial function Z(u) in many different contexts. It may contain experimental data (such as a map of terrain elevation) or computed values (such as a kernel estimate of point process intensity) or it may be directly obtained from a camera (such as a satellite image). 10.1 Creating a pixel image 10.1.1 Creating an image from raw data To create a pixel image from raw data, use im: > im(mat, xcol, yrow) where mat is a matrix containing the pixel values. The pixel values could have been generated by hand, or read from a file. The correspondence between matrix indices mat[i,j] and cartesian coordinates is slightly idiosyncratic: the rows ofmcorrespond to the y coordinate, and the columns to the x coordinate. The argument xcol is a vector of equally-spaced x coordinate values corresponding to the columns of mat, and yrow is a vector of equally-spaced y coordinate values corresponding to the rows of mat. These vectors determine the spatial position of the pixel grid. The length of xcol is ncol(mat) while the length of yrow is nrow(mat). If mat is not a matrix, it will be converted into a matrix with nrow(mat) = length(yrow) and ncol(mat) = length(xcol). > vec mat noisy plot(noisy) noisy −5 0 5 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
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 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: 9.5 List of operations on point pat
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
Page 85 and 86: 1 1 2 4 4 1 2 13.4 Distance map 85
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
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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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