What determines travel time and distance decay in spatial interaction and accessibility?

The concept of ‘distance decay’ curves is used in spatial interaction and accessibility analysis to represent the diminishing likelihood of visiting places with increasing travel impedance, mainly distance and travel time. The shape of the resulting impedance decay curves varies by several factors, but these influential factors are often dismissed in favor of just travel mode. In this study, we examine which factors should be used to distinguish impedance functions for use. Using data from a large national travel survey, we first show that the impedance curves are well approximated by functions of the exponential family and the related Tanner function. We use two methods – variable-wise function fit and Shapley additive explanations – to conclude the importance of four factors for developing impedance functions. These are travel mode, trip purpose, urbanity class of trip origin and destination, and the socioeconomic status grouping of the travelers. We then show that the use of a generalized impedance function can significantly over- or underestimate spatial accessibility compared to factor-specific impedance function, with up to 80 % overestimation on average in the case of public transit and 16 % overestimation for low socio-economic status travelers. These findings highlight the importance of the choice of impedance function which has applications in spatial economics, transportation planning, and human mobility analyses.