Morphisms for Quantitative Spatial Analysis (eBook)

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.

Preamble ………………………………………………………………………………………………..8Chapter 1 Introduction to Part 1: Spatial Statistics............................................................................. 101.1 Introduction ........................................................................................................................... 101.2 Polish employment data: 2006-2013. .................................................................................... 101.3 Polish data quality ................................................................................................................. 111.4 Concluding comments........................................................................................................... 14Chapter 2 Spatial Autocorrelation and the p-Median Problem .......................................................... 152.1 Introduction ........................................................................................................................... 152.2 Eigenvector spatial filtering in a nutshell.............................................................................. 152.3 Imputing missing spatial data................................................................................................ 162.4 The location-allocation problem............................................................................................ 172.5 Location-allocation solutions in the presence of missing and imputed data ......................... 192.6 Relationships between spatial autocorrelation and solutions to location-allocation problems................................................................................................................................ 222.7 Concluding comments........................................................................................................... 26Chapter 3 Space-Time Autocorrelation.............................................................................................. 283.1 Introduction ........................................................................................................................... 283.2 Specifying a space-time Moran Coefficient .......................................................................... 283.3 Properties of the space-time Moran Coefficient.................................................................... 313.4 Eigenvector space-time filtering............................................................................................ 333.5 Omitted variables in a description of space-time response variables .................................... 353.6 Concluding comments........................................................................................................... 37Chapter 4 The Relative Importance of Spatial and Temporal Autocorrelation.................................. 384.1 Introduction ........................................................................................................................... 384.2 Random effects: SSRE and SURE components.................................................................... 404.3 Estimating a SURE term: a sensitivity analysis .................................................................... 424.4 Time beats space ................................................................................................................... 444.5 Space beats time .................................................................................................................... 454.6 Concluding comments........................................................................................................... 46Chapter 5 The Spatial Weights Matrix and ESF ................................................................................ 475.1 Introduction ........................................................................................................................... 475.2 Spatial weights matrix comparisons...................................................................................... 475.2.1 Some binary SWM comparisons ................................................................................... 495.2.2 Some row-standardized SWM comparisons.................................................................. 505.2.3 Variance stabilizing standardization.............................................................................. 515.3 Comparisons of spatial weights matrix eigenvectors ............................................................ 535.4 Competing model specifications: spatial autoregressions and ESFs..................................... 545.5 Concluding comments........................................................................................................... 56Chapter 6 Clustering: Spatial Autocorrelation and Location Quotients............................................. 576.1 Introduction ........................................................................................................................... 576.2 Location quotients (LQs)....................................................................................................... 576.3 The multivariate space-time structure of Polish LQs: 2006-2013......................................... 586.4 Spatial autocorrelation and LQs ............................................................................................ 596.5 Spatially adjusted LQs for Polish employment ..................................................................... 606.6 Space-time description of the Polish LQs ............................................................................. 626.7 Concluding comments ........................................................................................................... 65Chapter 7 Spatial Autocorrelation Parameter Estimation for Massively Large Georeferenced Datasets.............................................................................................................................. 667.1 Introduction ........................................................................................................................... 667.2 Maximum likelihood estimation............................................................................................ 667.2.1 A large remotely sensed image example ....................................................................... 687.2.2 Other approaches........................................................................................................... 697.3 The sampling variance of ρˆ .................................................................................................. 707.3.1 The asymptotic variance for massively large georeferenced datasets: the 1st-order eigenvalue term............................................................................................................. 737.3.2 The asymptotic variance for massively large georeferenced datasets: the 2nd-order eigenvalue term............................................................................................................. 747.3.3 The asymptotic variance for massively large georeferenced datasets: the residual term............................................................................................................................... 757.3.4 A preliminary asymptotic variance approximation accuracy assessment ..................... 767.4 Irregular surface partitioning spatial autocorrelation simulation experiments ...................... 767.5 Concluding comments........................................................................................................... 77Chapter 8 Space-Time Data and Semi-Saturated Fixed Effects......................................................... 798.1 Introduction ........................................................................................................................... 798.2 What is fixed effects? ............................................................................................................ 798.3 Testing for fixed effects......................................................................................................... 808.4 Fixed effects: SSFE and SUFE components ......................................................................... 818.5 Estimating a SUFE term: selected sensitivity analyses......................................................... 838.6 An exploration of interaction terms....................................................................................... 868.7 Concluding comments........................................................................................................... 86Chapter 9 Spatial Autocorrelation and Spatial Interaction Gravity Models....................................... 879.1 Introduction ........................................................................................................................... 879.2 The doubly-constrained gravity model: a Poisson specification that accounts for spatial autocorrelation ...................................................................................................................... 879.3 Modeling spatial autocorrelation........................................................................................... 889.4 Spatial autocorrelation and provincial-level journey-to-work flows..................................... 899.5 Infill and increasing domain analyses ................................................................................... 939.5.1 A comparative infill analysis of journey-to-work flows................................................ 939.5.2 A comparative increasing domain analysis of journey-to-work flows.......................... 969.6 Concluding comments ............................................................................................................ 97Chapter 10 General Conclusions About Spatial Statistics.................................................................... 9910.1 Introduction ........................................................................................................................... 9910.2 Spatial autocorrelation and the p-median problem................................................................ 9910.3 Space-time autocorrelation.................................................................................................. 10010.4 The relative importance of spatial and temporal autocorrelation........................................ 10010.5 The spatial weights matrix and eigenvector spatial filtering............................................... 10110.6 Clustering: spatial autocorrelation and location quotients .................................................. 10210.7 Spatial autocorrelation parameter estimation for massively large georeferenced datasets . 10310.8 Space-time data and semi-saturated fixed effects................................................................ 10410.9 Spatial autocorrelation and spatial interaction gravity models............................................ 10510.10 Concluding comments......................................................................................................... 105Chapter 11 Introduction to Part 2: Spatial Econometrics ................................................................... 107Chapter 12 Tinbergen-Bos Systems: Combining Combinatorial Analysis with Metric Topology.... 10812.1 Introduction ......................................................................................................................... 10812.2 TBS-analysis and first extensions ....................................................................................... 10912.2.1 Input-output relations (Kuiper and Paelinck, 1984) .................................................... 10912.2.2 Complexity (Paelinck, 2000b)..................................................................................... 11112.2.3 Hierarchy (Paelinck, 1995 and 1997, Part1)................................................................ 11112.2.4 Objective function ....................................................................................................... 11212.3 Metric extension.................................................................................................................. 11212.3.1 Manhattan circles and distance frequencies (Kuiper, Paelinck and Rosing 1990)...... 11212.3.2 Equations, weights....................................................................................................... 11312.3.3 Location-allocation aspects ......................................................................................... 11512.4 Endogenous number of plants with economies of scale and scope..................................... 11712.4.1 Economies of scale...................................................................................................... 11712.4.2 Economies of scope..................................................................................................... 11712.5 Non-unit prices .................................................................................................................... 11812.5.1 Price definition ............................................................................................................ 11812.5.2 Exogenous prices......................................................................................................... 11812.5.3 Endogenous prices....................................................................................................... 11912.6 Chapter conclusions ............................................................................................................ 12012.6.1 On theoretical spatial economics................................................................................. 12012.6.2 On spatial econometrics .............................................................................................. 122Chapter 13 Time, Space, or Econotimespace? ................................................................................... 12513.1 Conceptual analysis............................................................................................................. 12513.1.1 Time............................................................................................................................. 12513.1.2 Space ........................................................................................................................... 12613.1.3 Space-time? ................................................................................................................. 12713.1.4 Toward spatial econometrics....................................................................................... 12913.2 Space-time spatial econometrics ......................................................................................... 12913.2.1 Space-time relation...................................................................................................... 12913.2.2 Space and time misspecification in spatial econometrics............................................ 13013.3 Chapter conclusions ............................................................................................................ 139Chapter 14 Hybrid dynamical systems and control............................................................................ 14014.1 Theoretical model................................................................................................................ 14014.2 Spatial econometric specification........................................................................................ 14114.3 Control................................................................................................................................. 14414.4 Negotiation .......................................................................................................................... 14514.5 Chapter conclusions ............................................................................................................ 147Chapter 15 The W matrix revisited .................................................................................................... 14715.1 Consistent spatial modeling................................................................................................. 14815.2 Lotka-Volterra systems as generalized logistics. ................................................................ 15015.3 Characterizing the A matrix in an extended SAR model .................................................... 15215.4 Chapter conclusions. ........................................................................................................... 154Chapter 16 Clustering, some non-standard approaches...................................................................... 15516.1 Axiomatic basis ................................................................................................................... 15516.1.1 Clusters........................................................................................................................ 15516.1.2 Complexes ................................................................................................................... 15616.1.3 Corps ........................................................................................................................... 15616.1.4 Hierarchies................................................................................................................... 15716.1.5 Interwovenness............................................................................................................ 15816.2 Spatial econometrics............................................................................................................ 15916.2.1 Methodology ............................................................................................................... 15916.2.2 Applications and comparison ...................................................................................... 16316.3 Comparison of results.......................................................................................................... 16516.4 Chapter conclusions ............................................................................................................ 166Chapter 17 Linear expenditure systems and related estimation problems ......................................... 16717.1 Linear expenditure systems (Paelinck, 1964; Solari, 1971) ................................................ 16717.1.1 Level specification....................................................................................................... 16717.1.2 GRM1: growth rate model 1........................................................................................ 16817.1.3 GRM2: growth rate model 2........................................................................................ 16917.1.4 Conclusion................................................................................................................... 16917.2 Different estimators compared ............................................................................................ 16917.2.1 SDLS: Simultaneous Dynamic Least squares ............................................................. 17017.2.2 RF (Reduced Form) and 2SLS (Two Stage Least Squares) estimation....................... 17117.2.3 Latent Variables........................................................................................................... 17217.2.4 LES, linear expenditure systems ................................................................................. 17317.2.5 Conclusion................................................................................................................... 17317.3 Distribution-free maximum likelihood estimation .............................................................. 17417.3.1 Single equation case .................................................................................................... 17417.3.2 Interdependent systems ............................................................................................... 17517.4 Chapter conclusions. ........................................................................................................... 176Chapter 18 Structural indicators galore….......................................................................................... 17718.1 Spatial discount functions.................................................................................................... 17718.1.1 The Tanner function .................................................................................................... 17718.1.2 The Ancot-Paelinck function....................................................................................... 17818.1.3 The continuous Poisson function................................................................................. 17918.1.4 The Lognormal function.............................................................................................. 17918.1.5 The Loglogistic function ............................................................................................. 18018.1.6 Conclusions ................................................................................................................. 18018.2 Dispersion coefficients ........................................................................................................ 18118.2.1 Variance analysis......................................................................................................... 18218.2.2 Theil’s U coefficient generalized ................................................................................ 18318.2.3 Some trigonometry ...................................................................................................... 18318.2.4 Correlation analysis..................................................................................................... 18418.2.5 Synthesis...................................................................................................................... 18518.3 Chapter conclusions ............................................................................................................ 185Chapter 19 Traveling with the salesman... ......................................................................................... 18619.1 The Traveling Salesman Problem ....................................................................................... 18619.2 The Matrix Permutation Problem........................................................................................ 19019.3 The Koopmans-Beckmann problem.................................................................................... 19119.4 Dynamic cluster analysis..................................................................................................... 19119.5 Chapter conclusions ............................................................................................................ 194Chapter 20 Complexer and complexer, said Alice…......................................................................... 19520.1 Corps anew.......................................................................................................................... 19520.2 A topography of complexes................................................................................................. 19820.2.1 Circumscribing clusters ............................................................................................... 19820.2.2 Positioning plants ........................................................................................................ 20220.3 Metropolitan complexes ...................................................................................................... 20420.3.1 Statistical material ....................................................................................................... 20420.3.2 Complex analysis......................................................................................................... 20720.4 Chapter conclusions ............................................................................................................ 208Chapter 21 General conclusions about spatial econometrics ............................................................. 20921.1 Complexity .......................................................................................................................... 20921.2 Parameter relativity ............................................................................................................. 210Epilogue ......................................................................................................................................... 212References ......................................................................................................................................... 213Subject index....................................................................................................................................... 224Authors’ index..................................................................................................................................... 230