Morphisms for Quantitative Spatial Analysis

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