Sparse regression for data-driven deterrence functions in gravity models

Gravity models have been one of the mathematical models of choice for trip distribution modeling efforts during many decades. Their simplicity offset their drawbacks, as they usually provide a reasonably good rationale for how goods are distributed in a transportation network with relatively little information. These gravity models, however, rely on the definition of a deterrence function that acts as a counterweight of the levels of supply and demand. This function is usually picked from a series of off-the-shelf available functions that only depend on a handful of parameters that need to be calibrated. Because of the limited off-the shelf options, gravity models lack flexibility in some occasions. In this paper, we tackle the use of sparse regression techniques that can accommodate data more flexibly with a reduced number of terms. Using interregional freight origin–destination data from Spain, we test two alternatives, namely, best subset regression and lasso regression. We show that the first one performs better in finding parsimonious deterrence functions and we attain gravity models that fit the data up to 14.5% better than classical deterrence functions.