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Spatial Data Analysis in the Social and Environmental Sciences - Robert Haining

Spatial Data Analysis in the Social and Environmental Sciences

Paperback

Published: 25th October 1993
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A spatial data set is a data set in which each observation is referenced to a site or area. Within both the social and environmental sciences, much of the data collected is within a spatial context and requires statistical analysis for interpretation. The purpose of this book, therefore, is to describe to students and research workers in the social and environmental sciences the current methods available for the analyses of spatial data. Methods described include data description, map interpolation, exploratory and explanatory analyses. The book also examines how spatial referencing raises a distinctive set of issues for the data analyst and recognizes the need to test underlying statistical assumptions. Further, methods for detecting problems, assessing their seriousness and taking appropriate action are discussed.

' ... a landmark text.' Geography ' ... masterly summary of spatial analysis.' Physical Geography

List of tables and displaysp. xiii
Prefacep. xviii
Acknowledgementsp. xx
Introduction to issues in the analysis of spatially referenced data
Introductionp. 3
Notesp. 10
Issues in analysing spatial datap. 12
Spatial data: sources, forms and storagep. 13
Sources: quality and quantityp. 13
Forms and attributesp. 17
Data storagep. 18
Spatial data analysisp. 21
The importance of space in the social and environmental sciencesp. 21
Measurement errorp. 21
Continuity effects and spatial heterogeneityp. 22
Spatial processesp. 24
Types of analytical problemsp. 26
Problems in spatial data analysisp. 32
Conceptual models and inference frameworks for spatial datap. 32
Modelling spatial variationp. 37
Statistical modelling of spatial datap. 40
Dependency in spatial datap. 40
Spatial heterogeneity: regional subdivisions and parameter variationp. 43
Spatial distribution of data points and boundary effectsp. 44
Assessing model fitp. 45
Distributionsp. 46
Extreme data valuesp. 46
Model sensitivity to the areal systemp. 47
Size-variance relationships in homogeneous aggregatesp. 49
A statistical framework for spatial data analysisp. 50
Data adaptive modellingp. 50
Robust and resistant parameter estimationp. 54
Robust estimation of the centre of a symmetric distributionp. 55
Robust estimation of regression parametersp. 56
Notesp. 61
Parametric models for spatial variation
Statistical models for spatial populationsp. 65
Models for spatial populations: preliminary considerationsp. 66
Spatial stationarity and isotropyp. 66
Second order (weak) stationarity and isotropyp. 66
Second order (weak) stationarity and isotropy of differences from the meanp. 67
Second order (weak) stationarity and isotropy of incrementsp. 67
Order relationships in one and two dimensionsp. 69
Population models for continuous random variablesp. 75
Models for the mean of a spatial populationp. 75
Trend surface modelsp. 75
Regression modelp. 76
Models for second order or stochastic variation of a spatial populationp. 80
Interaction models for V of a MVN distributionp. 80
Interaction models for other multivariate distributionsp. 90
Direct specification of Vp. 90
Intrinsic random functionsp. 94
Population models for discrete random variablesp. 99
Boundary models for spatial populationsp. 101
Edge structures, weighting schemes and the dispersion matrixp. 110
Conclusions: issues in representing spatial variationp. 113
Notesp. 115
Simulating spatial modelsp. 116
Statistical analysis of spatial populationsp. 118
Model selectionp. 118
Statistical inference with interaction schemesp. 123
Parameter estimation: maximum likelihood (ML) methodsp. 123
[mu] unknown; V knownp. 123
[mu] known; V unknownp. 124
[mu] and V unknownp. 127
Models with non-constant variancep. 129
Parameter estimation: other methodsp. 130
Ordinary least squares and pseudo-likelihood estimatorsp. 130
Coding estimatorsp. 131
Moment estimatorsp. 133
Parameter estimation: discrete valued interaction modelsp. 134
Properties of ML estimatorsp. 134
Large sample propertiesp. 134
Small sample propertiesp. 135
A note on boundary effectsp. 137
Hypothesis testing for interaction schemesp. 142
Likelihood ratio testsp. 142
Lagrange multiplier testsp. 145
Statistical inference with covariance functions and intrinsic random functionsp. 147
Parameter estimation: maximum likelihood methodsp. 150
Parameter estimation: other methodsp. 151
Properties of estimators and hypothesis testingp. 154
Validation in spatial modelsp. 158
The consequences of ignoring spatial correlation in estimating the meanp. 161
Notesp. 166
Spatial data collection and preliminary analysis
Sampling spatial populationsp. 171
Introductionp. 171
Spatial sampling designsp. 175
Point samplingp. 175
Quadrat and area samplingp. 177
Sampling spatial surfaces: estimating the meanp. 177
Fixed populations with trend or periodicityp. 178
Populations with second order variationp. 178
Results for one-dimensional seriesp. 180
Results for two-dimensional surfacesp. 181
Standard errors for confidence intervals and selecting sample sizep. 183
Sampling spatial surfaces: second order variationp. 186
Krigingp. 186
Scales of variationp. 189
Sampling applicationsp. 191
Concluding commentsp. 195
Preliminary analysis of spatial datap. 197
Preliminary data analysis: distributional properties and spatial arrangementp. 198
Univariate data analysisp. 198
General distributional propertiesp. 200
Spatial outliersp. 214
Spatial trendsp. 215
Second order non-stationarityp. 222
Regional subdivisionsp. 223
Multivariate data analysisp. 223
Data transformationsp. 227
Preliminary data analysis: detecting spatial pattern, testing for spatial autocorrelationp. 228
Available test statisticsp. 228
Constructing a testp. 231
Interpretationp. 234
Choosing a testp. 237
Describing spatial variation: robust estimation of spatial variationp. 239
Robust estimators of the semi-variogramp. 241
Robust estimation of covariancesp. 244
Concluding remarksp. 244
Notesp. 245
Modelling spatial data
Analysing univariate data setsp. 249
Describing spatial variationp. 250
Non-stationary mean, stationary second order variation: trend surface models with correlated errorsp. 251
Non-stationary mean, stationary increments: semi-variogram models and polynomial generalised covariance functionsp. 282
Discrete datap. 288
Interpolation and estimating missing valuesp. 291
Ad hoc and cartographic techniquesp. 293
Distribution based techniquesp. 296
Sequential approaches (sampling a continuous surface)p. 297
Simultaneous approachesp. 304
Extensionsp. 307
Obtaining areal propertiesp. 307
Reconciling data sets on different areal frameworksp. 309
Categorical datap. 310
Other information for interpolationp. 310
Notesp. 311
Analysing multivariate data setsp. 313
Measures of spatial correlation and spatial associationp. 313
Correlation measuresp. 313
Measures of associationp. 324
Regression modellingp. 330
Problems due to the assumptions of least squares not being satisfiedp. 334
Problems of model specification and analysisp. 339
Model discriminationp. 341
Specifying Wp. 341
Parameter estimation and inferencep. 344
Model evaluationp. 347
Interpretation problemsp. 348
Problems due to data characteristicsp. 348
Numerical problemsp. 349
Regression applications
Model diagnostics and model revision (a) new explanatory variablesp. 350
Model diagnostics and model revision (b) developing a spatial regression modelp. 354
Regression modelling with census variables: Glasgow health datap. 365
Identifying spatial interaction and heterogeneity: Sheffield petrol price datap. 372
Notesp. 383
Robust estimation of the parameters of interaction schemesp. 384
Postscriptp. 386
Glossaryp. 389
Referencesp. 391
Indexp. 406
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521448666
ISBN-10: 0521448662
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 432
Published: 25th October 1993
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.3
Weight (kg): 0.61