A new method using medians to calibrate single-parameter spatial interaction models

Abstract

I present a method for calibrating the impedance parameter of a gravity spatial interaction model using only the median travel time as a measure of observed traveler behavior. Complete information about the spatial structure of origins, destinations, and travel times between origins and destinations is also required. Using Monte Carlo simulation techniques on stylized cities, I attempt to recover true (a priori known) impedance values with this method for a range of impedance values for both negative exponential and power impedance functions. The results are compared with estimates obtained by other fast methods. The proposed method proves to provide a fairly accurate estimate of the impedance parameter, with a mean percent error typically below 20% and often below 10% for common impedance values. The proposed method is an improvement over existing calibration methods in several respects. First, it allows for the estimation of the impedance parameter directly without lengthy iterative calculations. Second, because it only requires median travel times, it can be calibrated with smaller samples (n~200), allowing the construction of gravity models for specific modes and/or travel purposes. And third, the method does not require expensive travel demand software and so can be implemented more widely in practice.

Accessibility to various destinations by public and private transport in Szczecin

“…In Szczecin, which is a medium-sized city, the spatial resistance function includes shorter time distances. The most often used type of the spatial resistance function in potential accessibility studies is the exponential function (Beria et al, 2017;Stępniak, Goliszek, 2017;Thompson et al, 2019;Merlin, 2020), i.e. : 𝑓(𝑡 𝑖𝑗 ) = 𝑒𝑥𝑝(𝛽𝑡 𝑖𝑗 ), where β differentiates the level of destination attractiveness reduction.…”

GIS tools and programming languages for creating models of public and private transport potential accessibility in Szczecin, Poland

“…In this case, using more sharply falling function of spatial resistance will result in more densely populated areas being more visible on the map and the significance of the public transport system will be underestimated. Other researchers use the travel time median as a measure of passengers behaviour in order to calibrate the space resistance parameter for their models (Merlin 2020).…”

Διαστάσεις, Μέτρηση Και Εξέλιξη Της Γεωγραφικής Απομόνωσης Στην Ελλάδα

“…Τα μοντέλα χωρικής αλληλεπίδρασης είναι μαθηματικά μοντέλα, τα οποία βοηθούν στην περιγραφή και ανάλυση της πιθανότητας αλληλεπίδρασης στον χώρο (Merlin, 2020).…”

“…Υπάρχουν τέσσερα είδη βαρυτικών μοντέλων χωρικής αλληλεπίδρασης: τα μη περιορισμένα, τα περιορισμένα ως προς την αφετηρία, τα περιορισμένα ως προς την έλξη/προορισμό και τα διπλώς περιορισμένα (Fotheringham & O'Kelly, 1989;Merlin, 2020).…”

“…Τα μη περιορισμένα βαρυτικά μοντέλα χωρικής αλληλεπίδρασης περιγράφουν τις ροές F ij μεταξύ μιας τοποθεσίας αφετηρίας i και μιας τοποθεσίας προορισμού j σύμφωνα με την εξίσωση (Griffith, 2007;Sen & Smith, 2012): (Merlin, 2020). Πολύ σημαντικό τμήμα των τρόπων μέτρησης της προσβασιμότητας στηρίζεται στα μοντέλα χωρικής αλληλεπίδρασης.…”