Spatial Statistics and Geostatistics Theory and Applications for Geographic Information Science and Technology

Title Page......Page 4
Copyright......Page 6
Dedeication......Page 8
Table of Contents......Page 9
About the Authors......Page 12
Preface......Page 13
1.1. Spatial statistics and geostatistics......Page 15
1.2. R basics......Page 19
2 Spatial Autocorrelation......Page 22
2.1. Indices measuring spatial dependency......Page 24
2.1.1. Important properties of MC......Page 25
2.1.2. Relationships between MC and GR, and MC and join count statistics......Page 27
2.2. Graphic portrayals: the Moran scatterplot and the semi-variogram plot......Page 29
2.4. Testing for spatial autocorrelation in regression residuals......Page 32
2.5. R code for concept implementations......Page 34
3 Spatial Sampling......Page 37
3.1. Selected spatial sampling designs......Page 39
3.2. Puerto Rico DEM data......Page 41
3.3. Properties of the selected sampling designs: simulation experiment results......Page 44
3.3.1. Sampling simulation experiments on a unit square landscape......Page 45
3.3.2. Sampling simulation experiments on a hexagonal landscape structure......Page 47
3.4. Resampling techniques: reusing sampled data......Page 49
3.4.1. The bootstrap......Page 50
3.4.2. The jackknife......Page 51
3.5. Spatial autocorrelation and effective sample size......Page 53
3.6. R code for concept implementations......Page 55
4 Spatial Composition and Configuration......Page 59
4.1. Spatial heterogeneity: mean and variance......Page 60
4.1.1. ANOVA......Page 61
4.1.2. Testing for heterogeneity over a plane: regional supra-partitionings......Page 62
4.1.2.2. A null hypothesis rejection case with heterogeneity......Page 66
4.1.3. Testing for heterogeneity over a plane: directional supra-partitionings......Page 68
4.1.4. Covariates across a geographic landscape......Page 70
4.2.1. Weight matrices for geographic distributions......Page 73
4.3. Spatial heterogeneity: spatial autocorrelation......Page 75
4.3.1. Regional differences......Page 76
4.3.2. Directional differences: anisotropy......Page 77
4.4. R code for concept implementations......Page 80
5 Spatially Adjusted Regression and Related Spatial Econometrics......Page 84
5.1. Linear regression......Page 85
5.2. Nonlinear regression......Page 89
5.2.1. Binomial/logistic regression......Page 90
5.2.2.1. Geographic distributions......Page 93
5.2.2.2. Geographic flows: a journey-to-work example......Page 97
5.3. R code for concept implementations......Page 100
6 Local Statistics: Hot and Cold Spots......Page 108
6.1. Multiple testing with positively correlated data......Page 109
6.2. Local indices of spatial association......Page 111
6.3. Getis–Ord statistics......Page 114
6.4. Spatially varying coefficients......Page 115
6.5. R code for concept implementations......Page 117
7 Analyzing Spatial Variance and Covariance with Geostatistics and Related Techniques......Page 121
7.1. Semi-variogram models......Page 122
7.2.1. DEM elevation as a covariate......Page 125
7.2.2. Landsat 7 ETM+ data as a covariate......Page 127
7.3. Spatial linear operators......Page 128
7.3.1. Multivariate geographic data......Page 130
7.4. Eigenvector spatial filtering: correlation coefficient decomposition......Page 136
7.5. R code for concept implementations......Page 139
8 Methods for Spatial Interpolation in Two Dimensions......Page 148
8.1. Kriging: an algebraic basis......Page 150
8.2. The EM algorithm......Page 154
8.3. Spatial autoregression: a spatial EM algorithm......Page 157
8.4. Eigenvector spatial filtering: another spatial EM algorithm......Page 159
8.5. R code for concept implementations......Page 162
9 More Advanced Topics in Spatial Statistics......Page 172
9.1. Bayesian methods for spatial data......Page 174
9.1.1. Markov chain Monte Carlo techniques......Page 176
9.1.2. Selected Puerto Rico examples......Page 177
9.2.1. A Monte Carlo experiment investigating eigenvector selection when constructing a spatial filter......Page 185
9.2.2. A Monte Carlo experiment investigating eigenvector selection from a restricted candidate set of vectors......Page 187
9.3. Spatial error: a contributor to uncertainty......Page 189
9.4. R code for concept implementations......Page 190
References......Page 193
Index......Page 197