Gravity Models of Spatial Interaction Behavior

摘要: I Theoretical Development.- 1 Spatial Interaction Processes: An Overview.- 1.1 Introduction.- 1.2 Perspectives.- 1.2.1 Macro versus Micro Theories.- 1.2.2 Static Dynamic 1.2.3 Probabilistic Deterministic 1.3 Analytical Framework.- 1.3.1 Measures of Separation.- 1.3.2 Aggregation Assumptions.- 1.3.3 Structural Independence 1.4 Processes.- 1.4.1 Patterns.- 1.4.2 General 1.4.3 Independent 1.5 Relaxations Independence.- 1.5.1 Frequency 1.5.2 Locational 1.5.3 More Complex Types Interdependencies.- 2 Gravity Models: 2.1 2.2 Models.- 2.2.1 Model Specifications.- 2.2.2 Illustrative Examples.- 2.2.3 Behavioral Characterizations.- 2.3 Functional 2.3.1 Origin and Destination Functions.- 2.3.2 Deterrence 2.4 Exponential 2.4.1 2.4.2 2.4.3 2.5 Generalizations the 2.5.1 Generalized Search 2.5.2 Processes with Hierarchical Destinations.- 2.5.3 Random Sets.- 3 Formal 3.1 3.2 Preliminaries.- 3.2.1 Measurable Spaces.- 3.2.2 3.2.3 Probability 3.3 3.3.1 3.3.2 Attributes Interactions.- 3.3.3 Events.- 3.3.4 3.4 3.4.1 Separation Configurations.- 3.4.2 3.4.3 3.5 3.6 Generated 3.6.1 Poisson 3.6.2 Characterization Theorem.- 3.7 Threshold 3.7.1 Potential 3.7.2 3.7.3 3.8 3.8.1 3.8.2 Realized-Interaction Frequencies.- 3.8.3 3.9 3.9.1 3.9.2 Relaxation 3.9.3 3.10 Notes References.- 4 4.1 4.2 Definition Classes.- 4.2.1 4.2.2 4.2.3 Relationships Among Types.- 4.3 Examples 4.3.1 Carroll-Bevis 4.3.2 4.3.3 Kullback-Leibler 4.3.4 Simple 4.4 Axioms for 4.4.1 Positive 4.4.2 Axioms.- 4.4.3 Relations among 4.5 Characterizations 4.5.1 4.5.2 4.5.3 4.6 4.6.1 4.6.2 4.6.3 Prominence Effects.- 4.7 II Methods.- 5 Maximum Likelihood.- 5.1 5.1.1 5.1.2 Likelihood Estimation.- 5.1.3 A Preview this Chapter.- 5.2 Existence Uniqueness ML Estimates.- 5.2.1 Condition ML1.- 5.2.2 ML2.- 5.2.3 Proof Theorem 5.1.- 5.2.4 Estimation Multinomial 5.3 Algorithms: Special Cases.- 5.3.1 The DSF Procedure.- 5.3.2 Evans-Kirby 5.3.3 Hyman 5.4 LDSF 5.4.1 5.4.2 Approximation Useful Algorithms.- 5.4.3 Application to Short-term Forecasting.- 5.5 Algorithms 5.5.1 Scoring 5.5.2 Modified 5.5.3 Gradient Procedures.- 5.5.4 5.5.5 GLIM.- 5.6 Performance 5.6.1 Data.- 5.6.2 Convergence.- 5.6.3 Speeds 5.7 Covariance 5.7.1 $${\hat \theta _k}$$'s.- 5.7.2 $$ {\hat{T}_{{ij}}} $$.- 5.7.3 Other Forecasts.- 5.8 Goodness Fit.- 5.8.1 Global Measures.- 5.8.2 Residuals.- 5.9 Properties 5.9.1 Asymptotic Properties.- 5.9.2 Small Sample 5.9.3 Estimates from Factored 5.10 Concluding Remarks.- 5.10.1 Conclusion.- 6 Least Squares.- 6.1 6.1.1 6.2 LS 6.2.1 Reduction Parameters.- 6.2.2 Gauss-Markov Conditions.- 6.2.3 Bias.- 6.2.4 Weighting.- 6.2.5 6.3 Large Theory.- 6.3.1 6.3.2 Main 6.3.3 Projection Matrix.- 6.3.4 6.1.- 6.3.5 Some Practical Details.- 6.4 Alternative 6.4.1 Use Iterative Reweighting in Procedure 1.- 6.4.2 Not Reducing 6.4.3 OLS.- 6.4.4 Inverses.- 6.5 6.5.1 6.5.2 Simulations.- 6.5.3 Results 6.5.4 Conclusions.- 6.6 Non-linear 6.7 6.7.1 Appendix: Skokie List Principal Definitions Results.- Author Index.