Lecture 15 Spatial Interaction15-2 The Basic Gravity Model15-2 The Basic Gravity Model (Cont.)Slide 415-3 Evaluating Interactions15-3 Evaluating Interactions (Cont.)Slide 715-4 K – The Constant for Gravity Model19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC11Lecture 15 Spatial Interaction15-1 Intro to Spatial Interaction Modeling- Spatial diffusion ( Medical geography )- Huff Model (Market Delineation)- Gravity Model ( Migration, transportation, etc.)Interaction (such as traffic flows between cities) can be modeled with gravity formula.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC2215-2 The Basic Gravity Model15-2 The Basic Gravity ModelTwo most obvious factors which affect the amount of flow or interaction between any two points:(1) Population / GDP (Weight)(2) Distance / Driving Time (Distance)And gravity model can take them as input to evaluate the interaction between two points.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC3315-2 The Basic Gravity Model 15-2 The Basic Gravity Model (Cont.)(Cont.)1,2,4 cities’ population are 1000000. City 3’s population is 500000. Which link has more traffic than the rest?19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC4415-2 The Basic Gravity Model 15-2 The Basic Gravity Model (Cont.)(Cont.)Generalizations:Expected interactions between an origin city i and a destination city j (Iij) will vary directly with the population of the destination city j (Pj) and inversely with the distance between i and j (dij). ijjijdPI /^19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC5515-3 Evaluating Interactions15-3 Evaluating Interactions2500/1000000250/1000000//12214412^14^dPdPII19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC6615-3 Evaluating Interactions 15-3 Evaluating Interactions (Cont.)(Cont.)Further step to make the formula more general – add the impact from origin:ijjiijdPPI /^From the improved formula, we will have more traffic, if the population of origin were to be increased to 5000000.19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC7715-3 Evaluating Interactions 15-3 Evaluating Interactions (Cont.)(Cont.).iteraction observedor actual the torefers j. and ibetween flow ofn predicatio model therefer to )/()(/^^^ijijijjiijijijjiijIIdPPfIfIdPPI19/1/1419/1/14Jun Liang, Geography @ UNCJun Liang, Geography @ UNC8815-4 K – The Constant for Gravity 15-4 K – The Constant for Gravity