Estimation of interregional freight flows with a gravity model by OLS estimation, Poisson and neural network specifications

Abstract

In this paper we compare three different specifications of gravity models for inter regional freight flow prediction. The most used specification with OLS estimation is compared with a model where data are assumed to be Poisson distributed. We also compare these with a Feed Forward Back Propagation Neural Network. Data consists of freight flows between Norwegian counties. The attribute describing the nodes is population and distance in kilometers gives the friction on transport links. Since we here only are interested in inter regional flows all intra regional flows are excluded. Results are also compared with an earlier study by Bergkvist and Westin (1997) were all data were used. Estimations indicate that OLS compared to Poisson and Neural Network specifications will produce worse predictions. However, the question on how to compare performance is not undisputable and of great importance since different measures can produce quite different results, not just in scale but also in ranking. When non-linear models are used the lack of a simple interpretable R-square measure as in linear regression is evident. We therefore use different measures of performance and discuss their pros and cons. Bergkvist E. and Westin L. (1997) Estimation of gravity models by OLS estimation, NLS estimation, Poisson and Neural Network specifications. Submitted to "Analytical advances in Transportation Systems and Spatial Dynamics." Eds. Gastaldi M. and Reggiani A.