## Quantitative Geography: Perspectives on Spatial Data AnalysisIntegrating a discussion of the application of quantitative methods with practical examples, this book explains the philosophy of the new quantitative methodologies and contrasts them with the methods associated with geography's `Quantitative Revolution' of the 1960s. Key issues discussed include: the nature of modern quantitative geography; spatial data; geographical information systems; visualization; local analysis; point pattern analysis; spatial regression; and statistical inference. Concluding with a review of models used in spatial theory, the authors discuss the current challenges to spatial data analysis. Written to be accessible, to communicate the diversity and excitement of recent thinking, |

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### Contents

Establishing the Boundaries | 1 |

12 What is quantitative geography? | 4 |

13 Applications of quantitative geography | 8 |

14 Recent developments in quantitative geography | 10 |

15 Summary | 13 |

Notes | 14 |

Spatial Data | 15 |

22 Spatial data capture | 16 |

553 Spatial expansion method results | 117 |

554 GWR results | 118 |

56 Measuring local relationships in spatial interaction models | 128 |

57 Summary | 129 |

Point Pattern Analysis | 130 |

62 Initial exploration | 132 |

622 Other exploratory plots | 134 |

623 Nongraphical approaches to point pattern exploration | 136 |

23 Spatial objects | 17 |

24 Location on the globe location on a plane | 18 |

25 Distance | 20 |

26 Representing spatial data | 21 |

27 Models for spatial data | 22 |

272 The raster model | 23 |

28 Programming with spatial data | 24 |

282 The use of complex numbers to represent spatial data | 25 |

210 Summary | 29 |

The Role of Geographical Information Systems | 30 |

32 Simple GISbased spatial analysis | 32 |

322 Feature selection by geometric intersection | 33 |

323 Buffering features | 34 |

union | 35 |

intersection | 37 |

326 Proximity | 38 |

327 Contiguity | 41 |

328 Interpolation and fields | 42 |

329 Density functions | 45 |

3210 Analysis on networks | 46 |

3211 Query | 49 |

331 Dataintegration and management | 51 |

332 Exploration | 54 |

333 Postmodelling visualization | 55 |

34 Problems | 58 |

342 Crossarea aggregation | 59 |

35 Linking higherorder types of spatial analysis to GIS | 61 |

36 A role for GIS? | 64 |

Exploring Spatial Data Visually | 65 |

42 Stem and leaf plots | 66 |

43 Boxplots | 68 |

44 Histograms | 70 |

45 Density estimates | 71 |

46 Maps | 72 |

47 The scatterplot matrix | 75 |

48 Linked plots | 77 |

49 Parallel coordinate plots | 80 |

410 RADVIZ | 82 |

411 Projection pursuit | 86 |

412 Summary | 91 |

Notes | 92 |

Local Analysis | 93 |

52 The nature of local variations in relationships | 94 |

53 Measuring local relationships in univariate data | 96 |

532 Other local measures of univariate spatial relationships | 97 |

54 Measuring local relationships in multivariate data | 102 |

541 Multilevel modelling | 103 |

542 The spatial expansion method | 106 |

543 Geographically weighted regression Consider a global regression model given by | 107 |

55 An empirical comparison of the spatial expansion method and GWR | 114 |

552 Global regression model results | 115 |

63 Modelling point patterns | 138 |

64 Firstorder intensity analysis | 144 |

641 Kernel density estimates | 146 |

65 Secondorder intensity analysis | 149 |

66 Comparing distributions | 154 |

661 Comparing kernel densities | 155 |

662 Comparing K functions | 157 |

663 Comparing a point pattern with a population at risk | 159 |

67 Conclusions | 160 |

Notes | 161 |

Spatial Regression and Geostatistical Models | 162 |

72 Autoregressive models | 166 |

721 Spatially autoregressive models | 167 |

722 Spatial moving average models | 169 |

73 Kriging | 171 |

732 A worked example | 175 |

733 Trend surfaces from kriging residuals | 176 |

74 Semiparametric smoothing approaches | 178 |

75 Conclusions | 182 |

Statistical Inference for Spatial Data | 184 |

82 Informal inference | 185 |

822 Data mining | 187 |

8221 Cluster analysis | 188 |

8222 Neural networks | 190 |

83 Formal inference | 193 |

832 Classical inference | 198 |

833 Experimental and computational inference | 201 |

8332 Experimental distributions and spatial autocorrelation | 204 |

8333 An empirical comparison of classical and experimental inference | 206 |

834 Model building and model testing | 210 |

84 Conclusions | 211 |

Spatial Modelling and the Evolution of Spatial Theory | 213 |

92 Spatial interaction as social physics 18601970 | 215 |

93 Spatial interaction as statistical mechanics 197080 | 217 |

94 Spatial interaction as aspatial information processing 198090 | 222 |

95 Spatial interaction as spatial information processing 1990 onwards | 225 |

96 Summary | 234 |

Notes | 235 |

Challenges in Spatial Data Analysis | 236 |

102 Current challenges | 237 |

1022 Spatial nonstationarity | 240 |

1023 Alternative inferential frameworks Bayes MCMC | 242 |

1024 Geometry | 243 |

proximity and accessibility | 244 |

1026 Merging space and time | 245 |

103 Training people to think spatially | 246 |

1032 Software | 247 |

Bibliography | 249 |

267 | |

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### Common terms and phrases

aggregated alternative analysis of spatial application approach aspatial attributes bandwidth Bayesian behaviour boundaries Brunsdon burglaries calibration Chapter clustering coefficients confidence interval consider coordinates correlation counts data set defined density estimate digitized distance Equation error terms example exploratory Fotheringham function Geocomputation Geographic Information Geographic Information Systems geographically weighted global grid hypothesis individual inference intensity kernel kriging matrix measure microstates multilevel modelling multivariate null hypothesis observed Openshaw outliers output parallel coordinates parameter estimates plot point data point pattern analysis polygon population population density probability problem PROFMAN projection pursuit quantitative geography RADVIZ random regression model relationships represents sample scatterplot second-order space spatial analysis spatial autocorrelation spatial choice spatial data analysis spatial distribution spatial interaction models spatial modelling spatial patterns spatial processes spatial variation square statistical study area surface techniques theoretical unemployment values variables variance-covariance matrix vector visualization zero zones