Using marginal impedance distributions to calibrate impedance functions for accessibility measurement: a theoretical and empirical analysis

Abstract

An essential component of any accessibility measure is an impedance function capturing the frictional impact of travel on activity participation. Such functions are commonly calibrated using the marginal distribution of the impedance variable, usually distance or time. However, this approach lacks a clear theoretical basis, and is affected by bias related to the fact that shorter trips have fewer available destinations than longer trips, meaning that trips with low impedance occur less frequently. This bias may explain the observed bell-shaped survival functions for impedance, which are often attributed to frictionless responses at lower impedance values. This paper develops a theoretical foundation for calibration to marginal impedance distributions, proposing a power function correction to isolate the bias from the impedance function during estimation. Empirical results show that applying near-linear correction terms leads to better-fitting distributions. The resultant impedance functions exhibit steeper decay, carrying important implications for accessibility measurement and policy interpretation.