Lecture 19 Modifications of the Basic Gravity Model 19-1 The Distance-Decay Parameter 2018/11/15 Jun Liang, Geography @ UNC

19-1 The Distance-Decay Parameter (Cont.) How to decided the distance exponent? Recall the example of Chicago phone calls, truck traffic, and air traffic. Variations in the distance exponent itself have become the subject of empirical study – Different time (years, months, days, or weeks.) Different types of travel Different commodities shipped Different regions 2018/11/15 Jun Liang, Geography @ UNC

19-1 The Distance-Decay Parameter (Cont.) Example of Chicago’s Beta value change over time: The decline in Chicago’s distance exponent represents the declining friction of distance in air transport as technological and economic changes that took place in latter part of the twentieth century. 2018/11/15 Jun Liang, Geography @ UNC

19-1 The Distance-Decay Parameter (Cont.) 2018/11/15 Jun Liang, Geography @ UNC

19-1 The Distance-Decay Parameter (Cont.) Changing parameters in spatial interaction models – Negative relationships VS. Positive relationships. See figure 7.24. 2018/11/15 Jun Liang, Geography @ UNC

19-1 The Distance-Decay Parameter (Cont.) 2018/11/15 Jun Liang, Geography @ UNC

19-1 The Distance-Decay Parameter (Cont.) Surface transportation shows greater sensitivity to distance than does air transportation. Distance exponents for the truck flows (Chicago) are approximately 2.0 British road and rail transport – 2.5 Air transport exponents are closer to 1.0 The study of changes in the Chicago air exponent suggests a value of less than one for large gateway cities 2018/11/15 Jun Liang, Geography @ UNC

19-2 Complementarity: Attractive and Propulsive Forces Distance Variances for the dependent variable: Airline traffic, Phone calls, etc. Population Functionalities Complementairty Other attractive forces 2018/11/15 Jun Liang, Geography @ UNC

19-2 Complementarity: Attractive and Propulsive Forces (Cont.) Complementairty will increase interaction between destinations and origins. Example: Ullman’s agriculture surplus and deficit example. Basic Gravity model works for general cases, and it is hardly exist. It is important to look for other forces. 2018/11/15 Jun Liang, Geography @ UNC