Spatial data analysis in the social and environmental sciences:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge u.a.
Cambridge Univ. Press
1993
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| Ausgabe: | 1. paperback ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXI, 409 S. Ill., graph. Darst., Kt. |
| ISBN: | 0521384168 0521448662 |
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| 245 | 1 | 0 | |a Spatial data analysis in the social and environmental sciences |c Robert Haining |
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Datensatz im Suchindex
| _version_ | 1804124004480450560 |
|---|---|
| adam_text | Titel: Spatial data analysis in the social and environmental sciences
Autor: Haining, Robert P
Jahr: 1993
Contents
List of tables and displays xiii
Preface xviii
Acknowledgements xx
PART A Introduction to issues in the analysis of spatially
referenced data
1 Introduction 3
Notes 10
2 Issues in analysing spatial data 12
2.1 Spatial data: sources, forms and storage 13
2.1.1 Sources: quality and quantity 13
2.1.2 Forms and attributes 17
2.1.3 Data storage 18
2.2 Spatial data analysis 21
2.2.1 The importance of space in the social and environmental 21
sciences
2.2.1 (a) measurement error 21
2.2.1 (b) continuity effects and spatial heterogeneity 22
2.2.1 (c) spatial processes 24
2.2.2 Types of analytical problems 26
2.3 Problems in spatial data analysis 32
Sections starred ( ) could be omitted at a first reading. Details in section 3.2 could be omitted as
weU.
Vii
Contents
2.3.1 Conceptual models and inference frameworks for
spatial data 32
2.3.2 Modelling spatial variation 37
2.3.3 Statistical modelling of spatial data 40
2.3.3 (a) dependency in spatial data 40
2.3.3 (b) spatial heterogeneity: regional subdivisions and
parameter variation 43
2.3.3 (c) spatial distribution of data points and boundary effects 44
2.3.3 (d) assessing model fit 45
2.3.3 (e) distributions 46
2.3.3 (f) extreme data values 46
2.3.3 (g) model sensitivity to the areal system 47
2.3.3 (h) size-variance relationships in homogeneous aggregates 49
2.4 A statistical framework for spatial data analysis 50
2.4.1 Data adaptive modelling 50
2.4.2 Robust and resistant parameter estimation 54
2.4.2 (a) robust estimation of the centre of a symmetric
distribution 55
2.4.2 (b) robust estimation of regression parameters 56
Notes 61
part B Parametric models for spatial variation
3 Statistical models for spatial populations 65
3.1 Models for spatial populations: preliminary considerations 66
3.1.1 Spatial stationarity and isotropy 66
3.1.1 (a) second order (weak) stationarity and isotropy 66
3.1.1 (b) second order (weak) stationarity and isotropy of
differences from the mean 67
3.1.1 (c) second order (weak) stationarity and isotropy of
increments 67
3.1.2 Order relationships in one and two dimensions 69
3.2 Population models for continuous random variables 75
3.2.1 Models for the mean of a spatial population 75
3.2.1 (a) trend surface models 75
3.2.1 (b) regression model 76
3.2.2 Models for second order or stochastic variation of a spatial
population 80
viii
Contents
3.2.2 (a) interaction models for V of a MVN distribution 80
*3.2.2 (b) interaction models for other multivariate distributions 90
3.2.2 (c) direct specification of V 90
3.2.2 (d) intrinsic random functions 94
*3.3 Population models for discrete random variables 99
*3.4 Boundary models for spatial populations 101
3.5 Edge structures, weighting schemes and the dispersion
matrix 110
3.6 Conclusions: issues in representing spatial variation 113
Notes 115
* Appendix: simulating spatial models 116
4 Statistical analysis of spatial populations 118
4.1 Model selection 118
4.2 Statistical inference with interaction schemes 123
4.2.1 Parameter estimation: maximum likelihood (ML) methods 123
4.2.1 (a) i unknown; V known 123
4.2.1 (b) |i known; V unknown 124
4.2.1 (c) n and V unknown 127
*4.2.1 (d) models with non-constant variance 129
4.2.2 Parameter estimation: other methods 130
4.2.2 (a) ordinary least squares and pseudo-likelihood
estimators 130
4.2.2 (b) coding estimators 131
4.2.2 (c) moment estimators 133
*4.2.3 Parameter estimation: discrete valued interaction models 134
*4.2.4 Properties of ML estimators 134
4.2.4 (a) large sample properties 134
4.2.4 (b) small sample properties 135
4.2.4 (c) a note on boundary effects 137
*4.2.5 Hypothesis testing for interaction schemes 142
4.2.5 (a) Likelihood ratio tests 142
4.2.5 (b) Lagrange multiplier tests 145
4.3 Statistical inference with covariance functions and
intrinsic random functions 147
4.3.1 Parameter estimation: maximum likelihood methods 150
ix
Contents
*4.3.2 Parameter estimation: other methods 151
*4.3.3 Properties of estimators and hypothesis testing 154
4.4 Validation in spatial models 158
4.5 The consequences of ignoring spatial correlation in
estimating the mean 161
Notes 166
part c Spatial data collection and preliminary analysis
5 Sampling spatial populations 171
5.1 Introduction 171
5.2 Spatial sampling designs 175
5.2.1 Point sampling 175
5.2.2. Quadrat and area sampling 177
5.3 Sampling spatial surfaces: estimating the mean 177
5.3.1 Fixed populations with trend or periodicity 178
5.3.2 Populations with second order variation 178
5.3.2 (a) results for one-dimensional series 180
5.3.2 (b) results for two-dimensional surfaces 181
5.3.3 Standard errors for confidence intervals and selecting
sample size 183
5.4 Sampling spatial surfaces: second order variation 186
5.4.1 Kriging 186
5.4.2 Scales of variation 189
5.5 Sampling applications 191
5.6 Concluding comments 195
6 Preliminary analysis of spatial data 197
6.1 Preliminary data analysis: distributional properties and
spatial arrangement 198
6.1.1 Univariate data analysis 198
6.1.1 (a) General distributional properties 200
6.1.1 (b) Spatial outliers 214
6.1.1 (c) Spatial trends 215
6.1.1 (d) Second order non-stationarity 222
6.1.1 (e) Regional subdivisions 223
x
Contents
6.1.2 Multivariate data analysis 223
6.1.3 Data transformations 227
6.2 Preliminary data analysis: detecting spatial pattern,
testing for spatial autocorrelation 228
6.2.1 Available test statistics 228
6.2.2 Constructing a test 231
6.2.3 Interpretation 234
6.2.4 Choosing a test 237
*6.3 Describing spatial variation: robust estimation of spatial
variation 239
6.3.1 Robust estimators of the semi-variogram 241
6.3.2 Robust estimation of covariances 244
6.4 Concluding remarks 244
Notes 245
PART D Modelling spatial data
7 Analysing univariate data sets 249
7.1 Describing spatial variation 250
7.1.1 Non-stationary mean, stationary second order variation:
trend surface models with correlated errors 251
7.1.2 Non-stationary mean, stationary increments: semi-
variogram models and polynomial generalised covariance
functions 282
*7.1.3 Discrete data 288
7.2 Interpolation and estimating missing values 291
7.2.1 Ad hoc and cartographic techniques 293
*7.2.2 Distribution based techniques 296
7.2.2 (a) Sequential approaches (sampling a continuous
surface) 297
7.2.2 (b) Simultaneous approaches 304
7.2.3 Extensions 307
7.2.3 (a) Obtaining areal properties 307
7.2.3 (b) Reconciling data sets on different areal frameworks 309
7.2.3 (c) Categorical data 310
7.2.3 (d) Other information for interpolation 310
Notes 311
xi
Contents
8 Analysing multivariate data sets 313
8.1 Measures of spatial correlation and spatial association 313
8.1.1 Correlation measures 313
8.1.2 Measures of association 324
8.2 Regression modelling 330
8.2.1 Problems due to the assumptions of least squares not
being satisfied 334
8.2.2 Problems of model specification and analysis 339
8.2.2 (a) Model discrimination 341
8.2.2 (b) Specifying W 341
8.2.2 (c) Parameter estimation and inference 344
8.2.2 (d) Model evaluation 347
8.2.3 Interpretation problems 348
8.2.4 Problems due to data characteristics 348
8.2.5 Numerical problems 349
8.3 Regression applications
Example 8.1: Model diagnostics and model revision
(a) new explanatory variables 350
Example 8.2: Model diagnostics and model revision
(b) developing a spatial regression model 354
Example 8.3: Regression modelling with census variables:
Glasgow health data 365
Example 8.4: Identifying spatial interaction and
heterogeneity: Sheffield petrol price data 372
Notes 383
*Appendix: Robust estimation of the parameters of
interaction schemes 384
Postscript 386
Glossary 389
References 391
Index 406
xii
List of tables and displays
Tables
2.1 A general framework for statistical analysis 13
2.2 Considerations in defining the spatial attributes of a
region and regional data prior to data analysis 39
2.3 Robust estimators: weighting functions 58
3.1 Spatial correlations for the stationary form of the single
parameter CAR model 104
3.2 Spatial correlations for the stationary form of the two
parameter CAR model 105
3.3 Spatial correlations for the stationary form of the single
parameter SAR model 106
3.4 Lag one (R(0,l)) correlations for finite lattice schemes 107
3.5 Modelling strategies for different forms of spatial
stationarity and non-stationarity 114
4.1 Arithmetic mean, variance and mean square error of
the exact ML estimator of the parameter of a first order
SAR model 137
4.2 Arithmetic mean and standard deviation of the exact
ML estimators of the parameter of a first order CAR
model and the surface mean 139
4.3 Arithmetic mean and standard deviation of the Whittle
estimator of the parameter of a first order stationary
CAR model 140
4.4 5% critical values for — 21nA obtained by simulation
methods 144
4.5 Percent power for likelihood ratio (LR) and Moran tests
for a first order SAR model 147
4.6 Standard error of/2 (4.4) and/I (4.7) 162
xiii
Tables and displays
4.7 Information loss as a percentage of total information
for each directional parameter of a first order trend
surface 165
6.1 Glasgow community medicine area data: standardised
mortality rates 199-200
6.2 Petrol price data: petrol stations in southwest Sheffield 208-9
6.3 Application of median polish to remotely sensed data:
area 1 217
6.4 Application of median polish to remotely sensed data:
area 2 219
6.5 Application of median polish to remotely sensed data:
area 3 220
6.6 Row and column D statistics for the residual values for
area 1 220
7.1 Ordinary least squares estimates for the zero order trend
surface model: pollution data 255
7.2 Lag spatial correlations for the least squares residuals
from the zero order trend surface model: pollution data 255
7.3 Ordinary least squares estimates for the first order
(linear) trend surface model: pollution data 256
7.4 Lag spatial correlations for the least squares residuals
from the first order (linear) trend surface model:
pollution data 256
7.5 Estimates using an SAR model for V in (7.2): order 0
model on pollution data 256
7.6 Estimates using an SAR model for V in (7.2): first order
model on pollution data 257
7.7 Maximum likelihood estimates for (7.2): zero order
model on pollution data 257
7.8 Maximum likelihood estimates for (7.2): first order
model on pollution data 257
7.9 Maximum likelihood estimates using an SAR model for
V in (7.2): second order model on pollution data 258
7.10 Glasgow health data: (a) contiguous CMAs 266-7
(b) digitised co-ordinates
for each CMA 268-9
7.11 Ordinary least squares estimates for the second order
trend surface model (7.1): cancer data 270
7.12 Maximum likelihood estimates for the second order
trend surface model (7.2): cancer data 276
7.13 Leverage values for CMAs 276
xiv
Tables and displays
7.14 Population weighted second order trend surface model
(7.2): cancer data 279
7.15 Possible outliers: area 1 pollution data 281
7.16 Possible outliers: area 1 pollution data after adjusting
for initial outliers 283
7.17 Possible outliers: area 1 pollution data {a) after square
root transformation, (b) after square root
transformation of outlier adjusted data 283
7.18 Model fits: pollution data (area 1) 285
7.19 Fitting orders of logistic and autologistic model to TB
control adoption data 291
7.20 Estimated population density based on all other states
(worst cases only) 296
7.21 Henley s example 303
7.22 Missing value estimates: different forms for V. Case (a)
CAR model; case (b) Estimated empirical covariances 308
8.1 (a) Asymptotic value of n Var(r) when Yt and Y2 are
first order CAR models 315
(b) Asymptotic value of n Var(r) when Y^ and Y2 are
first order SAR models 316
8.2 Type I errors for a 5% test on the Pearson product
moment correlation coefficient based on 300
simulations of first order SAR processes. The upper
figure is the unadjusted test and the lower figure is the
test based on the Clifford and Richardson (1985)
adjustment (a) 11 x 11, (b)7x7 319
8.3 Properties of N for different levels of spatial dependence
in Yl and Y2. The Pearson product moment correlation
coefficient (1) 11 x 11 (n=-121) (2)7x7(n = 49) 320
8.4 Type I errors for a 5% test on the Spearman rank
correlation coefficient based on 300 simulations of first
order SAR processes converted to rank order values.
The upper figure is the unadjusted test and the lower
figure is the test based on the Clifford and Richardson
(1985) adjustment, (a) 11x11 (b)7*7 322
8.5 Properties of N for different levels of spatial dependence
in Yi and Y2. The Spearman rank correlation coeffi¬
cient (a) 11x11 (n= 121) (fr)7x7(n = 49) 323
8.6 Spearman s rank correlation measure for the 1980 and
1981 burglary data adjusted for the spatial structure of
the data 33°
xv
Tables and displays
8.7 Problems that may arise in fitting the regression model
using ordinary least squares: (a) Problems due to
assumptions of least squares (b) Problems due to the
nature of the data 332-3
8.8 Population density data (1970) for the 48 states in
Weisberg (1985) table 2.1 354
8.9 Ordinary least squares analysis of Irish data (a) Lag
correlations computed for the residuals
(b) Autocorrelation tests on the residuals 356
8.10 Fitting different spatial regression models to Irish
data (a) Lagged explanatory variable regression
model (b) Lagged response variable regression model 358
8.11 Fitting model (8.12) to the Irish data (a) SAR
errors (b) Other spatial error models 360
8.12 Leverage values (as % of total leverage) for model
(8.11) and model (8.12) with V = VSAR, W the
weighted form 362
8.13 Robust estimation of (8.12) for p using Tukey s bi-
weight 365
8.14 Glasgow CMA data 367
8.15 Diagnostics for the fit in Display 8.4 368
8.16 Testing for spatial heterogeneity in the petrol price data 382-3
Displays
6.1 First two moments of autocorrelation statistics 233
8.1 Analysis of US fuel consumption data (a) Model
fit (b) Diagnostics (c) Revised model 351
8.2 Evaluating the effects on parameter estimates of
deleting two counties (Donegal and Mayo) with high
leverages 362
8.3 Exploratory fit of census variables to Glasgow health
data: least squares fit 366
8.4 Fitting models to the cancer SMR data (1) Fitting
with additional quadratic trend: least squares
fit. (2) Fitting with non-constant error variance
(weighted least squares). (3) Fitting with additional
quadratic trend: resistant R-regression. (4) Stepwise
Poisson log linear regression 370-1
8.5 Analysis of petrol price data: temporal model I 376
8.6 Analysis of petrol price data: temporal model II 378
xvi
Tables and displays
8.7 Analysis of petrol price data: spatial models (a) Spatial
error model (V = VSAR) (fc) Lagged response variable
model 379
8.8 Robust estimation of spatial error model with V = VSAR
(a) Robust estimation of P only (b) Robust estimation
ofjSandp 379
xvU
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| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV009660960 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:38:46Z |
| institution | BVB |
| isbn | 0521384168 0521448662 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006388054 |
| oclc_num | 38076432 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-945 DE-703 DE-M49 DE-BY-TUM DE-83 DE-11 |
| owner_facet | DE-19 DE-BY-UBM DE-945 DE-703 DE-M49 DE-BY-TUM DE-83 DE-11 |
| physical | XXI, 409 S. Ill., graph. Darst., Kt. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Haining, Robert P. Verfasser aut Spatial data analysis in the social and environmental sciences Robert Haining 1. paperback ed. Cambridge u.a. Cambridge Univ. Press 1993 XXI, 409 S. Ill., graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Geografia da populacao larpcal Population geography Statistical methods Spatial analysis (Statistics) Bevölkerungsstatistik (DE-588)4006298-3 gnd rswk-swf Datenauswertung (DE-588)4131193-0 gnd rswk-swf Umweltwissenschaften (DE-588)4137364-9 gnd rswk-swf Statistische Analyse (DE-588)4116599-8 gnd rswk-swf Regionalanalyse (DE-588)4299244-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Raumdaten (DE-588)4206012-6 gnd rswk-swf Bevölkerungsgeografie (DE-588)4006293-4 gnd rswk-swf Räumliche Verteilung (DE-588)4121550-3 gnd rswk-swf Methode (DE-588)4038971-6 gnd rswk-swf Bevölkerungsgeografie (DE-588)4006293-4 s Datenauswertung (DE-588)4131193-0 s DE-604 Raumdaten (DE-588)4206012-6 s Statistische Analyse (DE-588)4116599-8 s Regionalanalyse (DE-588)4299244-8 s Sozialwissenschaften (DE-588)4055916-6 s Umweltwissenschaften (DE-588)4137364-9 s Statistik (DE-588)4056995-0 s 1\p DE-604 Räumliche Verteilung (DE-588)4121550-3 s Methode (DE-588)4038971-6 s 2\p DE-604 3\p DE-604 Bevölkerungsstatistik (DE-588)4006298-3 s 4\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006388054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Haining, Robert P. Spatial data analysis in the social and environmental sciences Geografia da populacao larpcal Population geography Statistical methods Spatial analysis (Statistics) Bevölkerungsstatistik (DE-588)4006298-3 gnd Datenauswertung (DE-588)4131193-0 gnd Umweltwissenschaften (DE-588)4137364-9 gnd Statistische Analyse (DE-588)4116599-8 gnd Regionalanalyse (DE-588)4299244-8 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Raumdaten (DE-588)4206012-6 gnd Bevölkerungsgeografie (DE-588)4006293-4 gnd Räumliche Verteilung (DE-588)4121550-3 gnd Methode (DE-588)4038971-6 gnd |
| subject_GND | (DE-588)4006298-3 (DE-588)4131193-0 (DE-588)4137364-9 (DE-588)4116599-8 (DE-588)4299244-8 (DE-588)4056995-0 (DE-588)4055916-6 (DE-588)4206012-6 (DE-588)4006293-4 (DE-588)4121550-3 (DE-588)4038971-6 |
| title | Spatial data analysis in the social and environmental sciences |
| title_auth | Spatial data analysis in the social and environmental sciences |
| title_exact_search | Spatial data analysis in the social and environmental sciences |
| title_full | Spatial data analysis in the social and environmental sciences Robert Haining |
| title_fullStr | Spatial data analysis in the social and environmental sciences Robert Haining |
| title_full_unstemmed | Spatial data analysis in the social and environmental sciences Robert Haining |
| title_short | Spatial data analysis in the social and environmental sciences |
| title_sort | spatial data analysis in the social and environmental sciences |
| topic | Geografia da populacao larpcal Population geography Statistical methods Spatial analysis (Statistics) Bevölkerungsstatistik (DE-588)4006298-3 gnd Datenauswertung (DE-588)4131193-0 gnd Umweltwissenschaften (DE-588)4137364-9 gnd Statistische Analyse (DE-588)4116599-8 gnd Regionalanalyse (DE-588)4299244-8 gnd Statistik (DE-588)4056995-0 gnd Sozialwissenschaften (DE-588)4055916-6 gnd Raumdaten (DE-588)4206012-6 gnd Bevölkerungsgeografie (DE-588)4006293-4 gnd Räumliche Verteilung (DE-588)4121550-3 gnd Methode (DE-588)4038971-6 gnd |
| topic_facet | Geografia da populacao Population geography Statistical methods Spatial analysis (Statistics) Bevölkerungsstatistik Datenauswertung Umweltwissenschaften Statistische Analyse Regionalanalyse Statistik Sozialwissenschaften Raumdaten Bevölkerungsgeografie Räumliche Verteilung Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006388054&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hainingrobertp spatialdataanalysisinthesocialandenvironmentalsciences |