Morphisms for Quantitative Spatial Analysis

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 Ï .................................................................................................. 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