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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.
Part I Spatial Statistics
1 Introduction to Part I: Spatial Statistics
3(6)
1.1 Introduction
3(1)
1.2 Polish Employment Data: 2006--2013
4(1)
1.3 Polish Data Quality
5(1)
1.4 Concluding Comments
6(3)
2 Spatial Autocorrelation and the p-Median Problem
9(16)
2.1 Introduction
9(1)
2.2 Eigenvector Spatial Filtering in a Nutshell
9(1)
2.3 Imputing Missing Spatial Data
10(2)
2.4 The Location--Allocation Problem
12(2)
2.5 Location--Allocation Solutions in the Presence of Missing and Imputed Data
14(4)
2.6 Relationships Between Spatial Autocorrelation and Solutions to Location-Allocation Problems
18(5)
2.7 Concluding Comments
23(2)
References
23(2)
3 Space-Time Autocorrelation
25(10)
3.1 Introduction
25(1)
3.2 Specifying a Space-Time Moran Coefficient
25(2)
3.3 Properties of the Space-Time Moran Coefficient
27(3)
3.4 Eigenvector Space-Time Filtering
30(2)
3.5 Omitted Variables in a Description of Space-Time Response Variables
32(1)
3.6 Concluding Comments
33(2)
References
34(1)
4 The Relative Importance of Spatial and Temporal Autocorrelation
35(14)
4.1 Introduction
35(1)
4.2 Random Effects: SSRE and SURE Components
36(5)
4.3 Estimating a SURE Term: A Sensitivity Analysis
41(2)
4.4 Time Beats Space
43(1)
4.5 Space Beats Time
43(4)
4.6 Concluding Comments
47(2)
References
47(2)
5 The Spatial Weights Matrix and ESF
49(12)
5.1 Introduction
49(1)
5.2 Spatial Weights Matrix Comparisons
49(7)
5.2.1 Some Binary SWM Comparisons
52(2)
5.2.2 Some Row-Standardized SWM Comparisons
54(1)
5.2.3 Variance Stabilizing Standardization
55(1)
5.3 Comparisons of Spatial Weights Matrix Eigenvectors
56(2)
5.4 Competing Model Specifications: Spatial Autoregressions and ESFs
58(1)
5.5 Concluding Comments
59(2)
References
60(1)
6 Clustering: Spatial Autocorrelation and Location Quotients
61(12)
6.1 Introduction
61(1)
6.2 Location Quotients
61(1)
6.3 The Multivariate Space-Time Structure of Polish LQs: 2006--2013
62(2)
6.4 Spatial Autocorrelation and LQs
64(1)
6.5 Spatially Adjusted LQs for Polish Employment
65(1)
6.6 Space-Time Description of the Polish LQs
66(1)
6.7 LQ Spatial Clusters in the Clustering of Employment
66(4)
6.8 Concluding Comments
70(3)
References
70(3)
7 Spatial Autocorrelation Parameter Estimation for Massively Large Georeferenced Datasets
73(16)
7.1 Introduction
73(1)
7.2 Maximum Likelihood Estimation
73(6)
7.2.1 A Large Remotely Sensed Image Example
75(3)
7.2.2 Other Approaches
78(1)
7.3 The Sampling Variance of p
79(6)
7.3.1 The Asymptotic Variance for Massively Large Georeferenced Datasets: The First-Order Eigenvalue Term
81(2)
7.3.2 The Asymptotic Variance for Massively Large Georeferenced Datasets: The Second-Order Eigenvalue Term
83(1)
7.3.3 The Asymptotic Variance for Massively Large Georeferenced Datasets: The Residual Term
84(1)
7.3.4 A Preliminary Asymptotic Variance Approximation Accuracy Assessment
85(1)
7.4 Irregular Surface Partitioning Spatial Autocorrelation Simulation Experiments
85(1)
7.5 Concluding Comments
86(3)
References
87(2)
8 Space-Time Data and Semi-saturated Fixed Effects
89(10)
8.1 Introduction
89(1)
8.2 What Is Fixed Effects?
90(1)
8.3 Testing for Fixed Effects
91(1)
8.4 Fixed Effects: SSFE and SUFE Components
91(2)
8.5 Estimating a SUFE Term: Selected Sensitivity Analyses
93(2)
8.6 An Exploration of Interaction Terms
95(2)
8.7 Concluding Comments
97(2)
References
97(2)
9 Spatial Autocorrelation and Spatial Interaction Gravity Models
99(14)
9.1 Introduction
99(1)
9.2 The Doubly Constrained Gravity Model: A Poisson Specification That Accounts for Spatial Autocorrelation
99(1)
9.3 Modeling Spatial Autocorrelation
100(2)
9.4 Spatial Autocorrelation and Provincial-Level Joumey-to-Work Flows
102(2)
9.5 Infill and Increasing Domain Analyses
104(6)
9.5.1 A Comparative Infill Analysis of Journey-to-Work Flows
106(3)
9.5.2 A Comparative Increasing Domain Analysis of Journey-to-Work Flows
109(1)
9.6 Concluding Comments
110(3)
References
112(1)
10 General Conclusions About Spatial Statistics
113(12)
10.1 Introduction
113(1)
10.2 Spatial Autocorrelation and the p-Median Problem
113(1)
10.3 Space-Time Autocorrelation
114(1)
10.4 The Relative Importance of Spatial and Temporal Autocorrelation
115(1)
10.5 The Spatial Weights Matrix and Eigenvector Spatial Filtering
115(2)
10.6 Clustering: Spatial Autocorrelation and Location Quotients
117(1)
10.7 Spatial Autocorrelation Parameter Estimation for Massively Large Georeferenced Datasets
118(1)
10.8 Space-Time Data and Semi-saturated Fixed Effects
119(1)
10.9 Spatial Autocorrelation and Spatial Interaction Gravity Models
120(1)
10.10 Concluding Comments
120(5)
References
121(4)
Part II Spatial Econometrics
11 Introduction to Part II: Spatial Econometrics
125(2)
Reference
126(1)
12 Tinbergen-Bos Systems: Combining Combinatorial Analysis with Metric Topology
127(22)
12.1 Introduction
128(1)
12.2 TBS Analysis and First Extensions
128(4)
12.2.1 Input-Output Relations (Kuiper and Paelinck 1984)
129(1)
12.2.2 Complexity (Paelinck 2000b)
130(1)
12.2.3 Hierarchy (Paelinck 1995, 1997, Part 1)
131(1)
12.2.4 Objective Function
132(1)
12.3 Metric Extension
132(5)
12.3.1 Manhattan Circles and Distance Frequencies (Kuiper et al. 1990)
132(1)
12.3.2 Equations and Weights
133(3)
12.3.3 Location-Allocation Aspects
136(1)
12.4 The Endogenous Number of Plants with Economies of Scale and Scope
137(1)
12.4.1 Economies of Scale
137(1)
12.4.2 Economies of Scope
138(1)
12.5 Non-unit Prices
138(3)
12.5.1 Price Definition
139(1)
12.5.2 Exogenous Prices
139(1)
12.5.2.1 Fixed Coefficients
139(1)
12.5.2.2 Variable Coefficients
140(1)
12.5.2.3 Economies of Scale and Scope
140(1)
12.5.3 Endogenous Prices
140(1)
12.6 Conclusions
141(5)
12.6.1 On Theoretical Spatial Economics
142(1)
12.6.2 On Spatial Econometrics
143(3)
References
146(3)
13 Time, Space, or Econotimespace?
149(18)
13.1 A Conceptual Analysis
149(4)
13.1.1 Time
149(1)
13.1.2 Space
150(2)
13.1.3 Space-Time, Rather Than Just Space or Time?
152(1)
13.1.4 Toward Spatial Econometrics
153(1)
13.2 Space--Time Spatial Econometrics
153(12)
13.2.1 Space--Time Relations
154(1)
13.2.2 Space and Time Misspecification in Spatial Econometrics
155(1)
13.2.2.1 The Problem
155(2)
13.2.2.2 Specifications
157(2)
13.2.2.3 Simulations
159(1)
13.2.2.4 Solutions
160(2)
13.2.2.5 Applications
162(1)
13.2.2.6 A General Approach
163(2)
13.2.2.7 Conclusions
165(1)
13.3
Chapter Conclusions
165(1)
References
165(2)
14 Hybrid Dynamical Systems and Control
167(10)
14.1 A Theoretical Model
167(1)
14.2 A Spatial Econometric Specification
168(4)
14.3 Control
172(1)
14.4 Negotiation
173(2)
14.5 Conclusions
175(1)
References
175(2)
15 The W Matrix Revisited
177(10)
15.1 Consistent Spatial Modeling
177(3)
15.2 Lotka-Volterra Systems as Generalized Logistic Models
180(2)
15.3 Characterizing the A Matrix in an Extended SAR Model
182(3)
15.4 Conclusions
185(1)
References
185(2)
16 Clustering: Some Nonstandard Approaches
187(14)
16.1 An Axiomatic Basis
187(5)
16.1.1 Clusters
187(1)
16.1.2 Complexes
188(1)
16.1.3 Corps
189(1)
16.1.4 Hierarchies
190(1)
16.1.5 Interwovenness
191(1)
16.2 Spatial Econometrics
192(7)
16.2.1 Methodology
192(1)
16.2.1.1 Connectropy (Kaashoek et al. 2004)
192(2)
16.2.1.2 Clustering (Paelinck 2004)
194(2)
16.2.2 Applications and Comparisons
196(1)
16.2.2.1 The Netherlands
196(1)
16.2.2.2 Belgium
197(2)
16.2.2.3 Comments
199(1)
16.3 Comparison of Results
199(1)
16.4 Conclusions
200(1)
References
200(1)
17 Linear Expenditure Systems and Related Estimation Problems
201(14)
17.1 Linear Expenditure Systems (Paelinck 1964; Solari 1971)
201(3)
17.1.1 Level Specification
201(2)
17.1.2 Growth Rate Model 1
203(1)
17.1.3 Growth Rate Model 2
204(1)
17.1.4 Conclusion
204(1)
17.2 Different Estimators Compared
204(6)
17.2.1 Simultaneous Dynamic Least Squares
205(1)
17.2.2 Reduced Form and Two Stage Least Squares Estimation
206(1)
17.2.3 Latent Variables
207(1)
17.2.4 Linear Expenditure Systems
208(2)
17.2.5 Conclusion
210(1)
17.3 Distribution-Free Maximum Likelihood Estimation
210(2)
17.3.1 The Single Equation Case
210(1)
17.3.2 Interdependent Systems
211(1)
17.4
Chapter Conclusions
212(1)
References
213(2)
18 Structural Indicators Galore
215(12)
18.1 Spatial Discount Functions
215(5)
18.1.1 The Tanner Function
215(2)
18.1.2 The Ancot-Paelinck Function
217(1)
18.1.3 The Continuous Poisson Function
217(1)
18.1.4 The Lognormal Function
218(1)
18.1.5 The Loglogistic Function
219(1)
18.1.6 Conclusions
219(1)
18.2 Dispersion Coefficients
220(5)
18.2.1 Variance Analysis
221(1)
18.2.2 Theil's U Coefficient Generalized
222(1)
18.2.3 Some Trigonometry
223(1)
18.2.4 Correlation Analysis
224(1)
18.2.5 Synthesis
224(1)
18.3
Chapter Conclusions
225(1)
References
225(2)
19 Traveling with the Salesman
227(10)
19.1 The Traveling Salesman Problem
227(4)
19.2 The Matrix Permutation Problem
231(1)
19.3 The Koopmans-Beckmann Problem
232(1)
19.4 Dynamic Cluster Analysis
233(2)
19.5
Chapter Conclusions
235(1)
References
235(2)
20 Complexer and Complexer, Said Alice
237(18)
20.1 Corps Anew
237(4)
20.2 A Topography of Complexes
241(7)
20.2.1 Circumscribing Clusters
241(1)
20.2.1.1 The Method
241(1)
20.2.1.2 Supporting Mathematics
242(4)
20.2.2 Positioning Plants
246(2)
20.3 Metropolitan Complexes
248(5)
20.3.1 Statistical Material
248(1)
20.3.1.1 The 1999 IMPLAN Database
248(1)
20.3.1.2 Arc View Business Analyst Datasets (Business Analyst 1999)
249(2)
20.3.2 Complex Analysis
251(1)
20.3.2.1 Identifying Complexes
251(1)
20.3.2.2 An Application to the Washington, DC Metropolitan Region
252(1)
20.4
Chapter Conclusions
253(1)
References
253(2)
21 General Conclusions About Spatial Econometrics
255(4)
21.1 Complexity
256(1)
21.2 Parameter Relativity
257(1)
References
257(2)
Epilogue 259(1)
References 260(1)
Author Index 261(4)
Subject Index 265
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 2009 to 2014. Among his many awards, he is a fellow of the Royal Society of Canada, the American Statistical Association, and the Guggenheim Foundation.  Jean H. P. Paelinck is an emeritus professor of the Erasmus University Rotterdam, and most recently was a distinguished Visiting Professor at George Mason University, VA, USA. As a (co-)author and (co-)editor, he has published around fifty volumes and over 400 articles, mainly on theoretical spatial economics and spatial econometrics. Paelinck has been awarded seven honorary PhDs and numerous other international distinctions, e.g. the Walter Isard Award in Regional Science.
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