Morphisms For Quantitative Spatial Analysis by Daniel A. GriffithMorphisms For Quantitative Spatial Analysis by Daniel A. Griffith

Morphisms For Quantitative Spatial Analysis

byDaniel A. Griffith, Jean H. P. Paelinck

Hardcover | March 15, 2018

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This book treats the notion of morphisms in spatial analysis, paralleling these concepts in spatial statistics (Part I) and spatial econometrics (Part II). The principal concept is morphism (e.g., isomorphisms, homomorphisms, and allomorphisms), which is defined as a structure preserving the functional linkage between mathematical properties or operations in spatial statistics and spatial econometrics, among other disciplines. The purpose of this book is to present selected conceptions in both domains that are structurally the same, even though their labelling and the notation for their elements may differ. As the approaches presented here are applied to empirical materials in geography and economics, the book will also be of interest to scholars of regional science, quantitative geography and the geospatial sciences. It is a follow-up to the book "Non-standard Spatial Statistics and Spatial Econometrics" by the same authors, which was published by Springer in 2011. 
Daniel A. Griffith , an Ashbel Smith Professor of Geospatial Information Science at the University of Texas at Dallas, TX, USA, has published 18 books and over 200 articles appearing in geography, statistics, mathematics, economics, and regional science journals and other outlets. Griffith served as editor of Geographical Analysis from...
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Title:Morphisms For Quantitative Spatial AnalysisFormat:HardcoverDimensions:258 pagesPublished:March 15, 2018Publisher:Springer NatureLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:3319725521

ISBN - 13:9783319725529

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Table of Contents

Preamble ..............................................................................................................8
Chapter 1 Introduction to Part 1: Spatial Statistics............................................................................. 10
1.1 Introduction ........................................................................................................................... 10
1.2 Polish employment data: 2006-2013. .................................................................................... 10
1.3 Polish data quality ................................................................................................................. 11
1.4 Concluding comments........................................................................................................... 14
Chapter 2 Spatial Autocorrelation and the p-Median Problem .......................................................... 15
2.1 Introduction ........................................................................................................................... 15
2.2 Eigenvector spatial filtering in a nutshell.............................................................................. 15
2.3 Imputing missing spatial data................................................................................................ 16
2.4 The location-allocation problem............................................................................................ 17
2.5 Location-allocation solutions in the presence of missing and imputed data ......................... 19
2.6 Relationships between spatial autocorrelation and solutions to location-allocation problems................................................................................................................................ 22
2.7 Concluding comments........................................................................................................... 26
Chapter 3 Space-Time Autocorrelation.............................................................................................. 28
3.1 Introduction ........................................................................................................................... 28
3.2 Specifying a space-time Moran Coefficient .......................................................................... 28
3.3 Properties of the space-time Moran Coefficient.................................................................... 31
3.4 Eigenvector space-time filtering............................................................................................ 33
3.5 Omitted variables in a description of space-time response variables .................................... 35
3.6 Concluding comments........................................................................................................... 37
Chapter 4 The Relative Importance of Spatial and Temporal Autocorrelation.................................. 38
4.1 Introduction ........................................................................................................................... 38
4.2 Random effects: SSRE and SURE components.................................................................... 40
4.3 Estimating a SURE term: a sensitivity analysis .................................................................... 42
4.4 Time beats space ................................................................................................................... 44
4.5 Space beats time .................................................................................................................... 45
4.6 Concluding comments........................................................................................................... 46
Chapter 5 The Spatial Weights Matrix and ESF ................................................................................ 47
5.1 Introduction ........................................................................................................................... 47
5.2 Spatial weights matrix comparisons...................................................................................... 47
5.2.1 Some binary SWM comparisons ................................................................................... 49
5.2.2 Some row-standardized SWM comparisons.................................................................. 50
5.2.3 Variance stabilizing standardization.............................................................................. 51
5.3 Comparisons of spatial weights matrix eigenvectors ............................................................ 53
5.4 Competing model specifications: spatial autoregressions and ESFs..................................... 54
5.5 Concluding comments........................................................................................................... 56
Chapter 6 Clustering: Spatial Autocorrelation and Location Quotients............................................. 57
6.1 Introduction ........................................................................................................................... 57
6.2 Location quotients (LQs)....................................................................................................... 57
6.3 The multivariate space-time structure of Polish LQs: 2006-2013......................................... 58
6.4 Spatial autocorrelation and LQs ............................................................................................ 59
6.5 Spatially adjusted LQs for Polish employment ..................................................................... 60
6.6 Space-time description of the Polish LQs ............................................................................. 62
6.7 Concluding comments ........................................................................................................... 65
Chapter 7 Spatial Autocorrelation Parameter Estimation for Massively Large Georeferenced Datasets.............................................................................................................................. 66
7.1 Introduction ........................................................................................................................... 66
7.2 Maximum likelihood estimation............................................................................................ 66
7.2.1 A large remotely sensed image example ....................................................................... 68
7.2.2 Other approaches........................................................................................................... 69
7.3 The sampling variance of ÏË .................................................................................................. 70
7.3.1 The asymptotic variance for massively large georeferenced datasets: the 1st-order eigenvalue term............................................................................................................. 73
7.3.2 The asymptotic variance for massively large georeferenced datasets: the 2nd-order eigenvalue term............................................................................................................. 74
7.3.3 The asymptotic variance for massively large georeferenced datasets: the residual term............................................................................................................................... 75
7.3.4 A preliminary asymptotic variance approximation accuracy assessment ..................... 76
7.4 Irregular surface partitioning spatial autocorrelation simulation experiments ...................... 76
7.5 Concluding comments........................................................................................................... 77
Chapter 8 Space-Time Data and Semi-Saturated Fixed Effects......................................................... 79
8.1 Introduction ........................................................................................................................... 79
8.2 What is fixed effects? ............................................................................................................ 79
8.3 Testing for fixed effects......................................................................................................... 80
8.4 Fixed effects: SSFE and SUFE components ......................................................................... 81
8.5 Estimating a SUFE term: selected sensitivity analyses......................................................... 83
8.6 An exploration of interaction terms....................................................................................... 86
8.7 Concluding comments........................................................................................................... 86
Chapter 9 Spatial Autocorrelation and Spatial Interaction Gravity Models....................................... 87
9.1 Introduction ........................................................................................................................... 87
9.2 The doubly-constrained gravity model: a Poisson specification that accounts for spatial autocorrelation ...................................................................................................................... 87
9.3 Modeling spatial autocorrelation........................................................................................... 88
9.4 Spatial autocorrelation and provincial-level journey-to-work flows..................................... 89
9.5 Infill and increasing domain analyses ................................................................................... 93
9.5.1 A comparative infill analysis of journey-to-work flows................................................ 93
9.5.2 A comparative increasing domain analysis of journey-to-work flows.......................... 96
9.6 Concluding comments ............................................................................................................ 97
Chapter 10 General Conclusions About Spatial Statistics.................................................................... 99
10.1 Introduction ........................................................................................................................... 99
10.2 Spatial autocorrelation and the p-median problem................................................................ 99
10.3 Space-time autocorrelation.................................................................................................. 100
10.4 The relative importance of spatial and temporal autocorrelation........................................ 100
10.5 The spatial weights matrix and eigenvector spatial filtering............................................... 101
10.6 Clustering: spatial autocorrelation and location quotients .................................................. 102
10.7 Spatial autocorrelation parameter estimation for massively large georeferenced datasets . 103
10.8 Space-time data and semi-saturated fixed effects................................................................ 104
10.9 Spatial autocorrelation and spatial interaction gravity models............................................ 105
10.10 Concluding comments......................................................................................................... 105
Chapter 11 Introduction to Part 2: Spatial Econometrics ................................................................... 107
Chapter 12 Tinbergen-Bos Systems: Combining Combinatorial Analysis with Metric Topology.... 108
12.1 Introduction ......................................................................................................................... 108
12.2 TBS-analysis and first extensions ....................................................................................... 109
12.2.1 Input-output relations (Kuiper and Paelinck, 1984) .................................................... 109
12.2.2 Complexity (Paelinck, 2000b)..................................................................................... 111
12.2.3 Hierarchy (Paelinck, 1995 and 1997, Part1)................................................................ 111
12.2.4 Objective function ....................................................................................................... 112
12.3 Metric extension.................................................................................................................. 112
12.3.1 Manhattan circles and distance frequencies (Kuiper, Paelinck and Rosing 1990)...... 112
12.3.2 Equations, weights....................................................................................................... 113
12.3.3 Location-allocation aspects ......................................................................................... 115
12.4 Endogenous number of plants with economies of scale and scope..................................... 117
12.4.1 Economies of scale...................................................................................................... 117
12.4.2 Economies of scope..................................................................................................... 117
12.5 Non-unit prices .................................................................................................................... 118
12.5.1 Price definition ............................................................................................................ 118
12.5.2 Exogenous prices......................................................................................................... 118
12.5.3 Endogenous prices....................................................................................................... 119
12.6 Chapter conclusions ............................................................................................................ 120
12.6.1 On theoretical spatial economics................................................................................. 120
12.6.2 On spatial econometrics .............................................................................................. 122
Chapter 13 Time, Space, or Econotimespace? ................................................................................... 125
13.1 Conceptual analysis............................................................................................................. 125
13.1.1 Time............................................................................................................................. 125
13.1.2 Space ........................................................................................................................... 126
13.1.3 Space-time? ................................................................................................................. 127
13.1.4 Toward spatial econometrics....................................................................................... 129
13.2 Space-time spatial econometrics ......................................................................................... 129
13.2.1 Space-time relation...................................................................................................... 129
13.2.2 Space and time misspecification in spatial econometrics............................................ 130
13.3 Chapter conclusions ............................................................................................................ 139
Chapter 14 Hybrid dynamical systems and control............................................................................ 140
14.1 Theoretical model................................................................................................................ 140
14.2 Spatial econometric specification........................................................................................ 141
14.3 Control................................................................................................................................. 144
14.4 Negotiation .......................................................................................................................... 145
14.5 Chapter conclusions ............................................................................................................ 147
Chapter 15 The W matrix revisited .................................................................................................... 147
15.1 Consistent spatial modeling................................................................................................. 148
15.2 Lotka-Volterra systems as generalized logistics. ................................................................ 150
15.3 Characterizing the A matrix in an extended SAR model .................................................... 152
15.4 Chapter conclusions. ........................................................................................................... 154
Chapter 16 Clustering, some non-standard approaches...................................................................... 155
16.1 Axiomatic basis ................................................................................................................... 155
16.1.1 Clusters........................................................................................................................ 155
16.1.2 Complexes ................................................................................................................... 156
16.1.3 Corps ........................................................................................................................... 156
16.1.4 Hierarchies................................................................................................................... 157
16.1.5 Interwovenness............................................................................................................ 158
16.2 Spatial econometrics............................................................................................................ 159
16.2.1 Methodology ............................................................................................................... 159
16.2.2 Applications and comparison ...................................................................................... 163
16.3 Comparison of results.......................................................................................................... 165
16.4 Chapter conclusions ............................................................................................................ 166
Chapter 17 Linear expenditure systems and related estimation problems ......................................... 167
17.1 Linear expenditure systems (Paelinck, 1964; Solari, 1971) ................................................ 167
17.1.1 Level specification....................................................................................................... 167
17.1.2 GRM1: growth rate model 1........................................................................................ 168
17.1.3 GRM2: growth rate model 2........................................................................................ 169
17.1.4 Conclusion................................................................................................................... 169
17.2 Different estimators compared ............................................................................................ 169
17.2.1 SDLS: Simultaneous Dynamic Least squares ............................................................. 170
17.2.2 RF (Reduced Form) and 2SLS (Two Stage Least Squares) estimation....................... 171
17.2.3 Latent Variables........................................................................................................... 172
17.2.4 LES, linear expenditure systems ................................................................................. 173
17.2.5 Conclusion................................................................................................................... 173
17.3 Distribution-free maximum likelihood estimation .............................................................. 174
17.3.1 Single equation case .................................................................................................... 174
17.3.2 Interdependent systems ............................................................................................... 175
17.4 Chapter conclusions. ........................................................................................................... 176
Chapter 18 Structural indicators galore............................................................................................. 177
18.1 Spatial discount functions.................................................................................................... 177
18.1.1 The Tanner function .................................................................................................... 177
18.1.2 The Ancot-Paelinck function....................................................................................... 178
18.1.3 The continuous Poisson function................................................................................. 179
18.1.4 The Lognormal function.............................................................................................. 179
18.1.5 The Loglogistic function ............................................................................................. 180
18.1.6 Conclusions ................................................................................................................. 180
18.2 Dispersion coefficients ........................................................................................................ 181
18.2.1 Variance analysis......................................................................................................... 182
18.2.2 Theil's U coefficient generalized ................................................................................ 183
18.2.3 Some trigonometry ...................................................................................................... 183
18.2.4 Correlation analysis..................................................................................................... 184
18.2.5 Synthesis...................................................................................................................... 185
18.3 Chapter conclusions ............................................................................................................ 185
Chapter 19 Traveling with the salesman... ......................................................................................... 186
19.1 The Traveling Salesman Problem ....................................................................................... 186
19.2 The Matrix Permutation Problem........................................................................................ 190
19.3 The Koopmans-Beckmann problem.................................................................................... 191
19.4 Dynamic cluster analysis..................................................................................................... 191
19.5 Chapter conclusions ............................................................................................................ 194
Chapter 20 Complexer and complexer, said Alice............................................................................ 195
20.1 Corps anew.......................................................................................................................... 195
20.2 A topography of complexes................................................................................................. 198
20.2.1 Circumscribing clusters ............................................................................................... 198
20.2.2 Positioning plants ........................................................................................................ 202
20.3 Metropolitan complexes ...................................................................................................... 204
20.3.1 Statistical material ....................................................................................................... 204
20.3.2 Complex analysis......................................................................................................... 207
20.4 Chapter conclusions ............................................................................................................ 208
Chapter 21 General conclusions about spatial econometrics ............................................................. 209
21.1 Complexity .......................................................................................................................... 209
21.2 Parameter relativity ............................................................................................................. 210
Epilogue ......................................................................................................................................... 212
References ......................................................................................................................................... 213
Subject index....................................................................................................................................... 224
Authors' index..................................................................................................................................... 230