Path Size Logit route choice models: Issues with current models, a new internally consistent approach, and parameter estimation on a large-scale network with GPS data

Abstract

Path Size Logit route choice models attempt to capture the correlation between routes by including correction terms within the route utility functions. This provides a convenient closed-form solution for implementation in traffic network models. The path size terms measure distinctiveness of routes; a route is penalised based on the number of other routes sharing its links, and the costs of those shared links. Typically, real road networks have many very long routes that should be considered unrealistic. Such unrealistic routes are problematic for the Path Size Logit (PSL) model because they negatively impact the choice probabilities of realistic routes when links are shared. The Generalised Path Size Logit (GPSL) model attempts to address this problem by weighting the contributions of routes to path size terms according to the ratio of route travel costs. However, the GPSL model is not internally consistent in how it defines routes as being unrealistic: the path size terms consider only travel cost, whereas the route choice probability relation considers disutility including the correction term. To solve these challenges, this paper formulates a new internally consistent Adaptive Path Size Logit (APSL) model wherein routes contribute to path size terms according to the ratio of route choice probabilities, ensuring that routes defined as unrealistic by the path size terms, are exactly those with very low choice probabilities. The APSL route choice probability relation is an implicit function, naturally expressed as a fixed-point problem. A proof is provided for the guaranteed existence of solutions, as well as conditions for the uniqueness of solutions. A Maximum Likelihood Estimation procedure is given for estimating the APSL model with tracked route observation data, and this procedure is investigated in a simulation study where it is shown it is generally possible to reproduce assumed true parameters. APSL is then estimated using real tracked route GPS data on a large-scale network, and results are compared with other PSL models.

The impact of COVID-19 pandemic on public transport usage and route choice: Evidences from a long-term tracking study in urban area

“…The PathSize was not found significant also in one of the experiments in Marra and Corman (2020) and in Nielsen et al (2021) . Doubts on the validity of the PathSize were also raised in Duncan et al (2020) , which demonstrate issues with this model. Therefore, we also estimated the model without this parameter, as a Mixed Logit (testing different correction parameters is out of the scope of this work).…”

A bounded path size route choice model excluding unrealistic routes: formulation and estimation from a large-scale GPS study

“…To combat this, Ramming (2002) proposed the Generalised Path Size Logit (GPSL) model where 𝑊 𝑘 = 𝑐 𝑘 −𝜆 and routes contribute according to travel cost ratios, so that routes with excessively large travel costs have a diminished impact upon the correction terms of routes with small travel costs, and consequently the choice probabilities of those routes. Duncan et al (2020) reformulate the GPSL model (proposing the alternative GPSL model (GPSL′)) so that the contribution weighting resembles the probability relation, i.e. 𝑊 𝑘 = 𝑒 −𝜆𝑐 𝑘 .…”

“…This approach, however, leads to theoretical inconsistencies, since the route generation criteria is not consistent with the calculation of the choice probabilities among chosen routes. Moreover, in large-scale case studies, for example the study of eastern Denmark in Prato et al (2014), Rasmussen et al (2017), Duncan et al (2020), as well as in Section 7.4 of this paper, it is implausible to attempt to generate the exact choice sets of realistic routes, and instead choice sets are generated large enough so that one can be fairly certain the realistic alternatives are present, regardless of how many unrealistic routes are generated. This is problematic, since many correlation-based models are not choice set robust, and results are thus negatively influenced by the presence of the unrealistic routes as well as highly sensitive to the choice set generation method adopted (Bovy et al, 2008;Bliemer & Bovy, 2008;Ramming, 2002;Ben-Akiva & Bierlaire, 1999;Bekhor et al (2008); Duncan et al, 2020).…”

“…Alternative RUMs to MNL either capture route correlations implicitly or utilise concepts from extended Logit models to similarly adapt the model. For a more detailed review, see Duncan et al (2020); however, we discuss the key models and concepts relevant to this paper below:…”

“…The pragmatic approach that has been proposed for addressing choice set robustness for PSL, is to utilise a weighted path size contribution technique along with choice set generation, to reduce the negative effects of any present unrealistic routes. The Generalised Path Size Logit (GPSL) model (Ramming, 2002) proposes a path size contribution factor based on travel cost ratios to reduce the contributions of costly routes, while the Adaptive Path Size Logit (APSL) model (Duncan et al, 2020) proposes a contribution factor based on choice probability ratios to provide internal consistency. While improving upon the choice set robustness of PSL, these approaches do not solve the issue entirely since the path size contributions of routes defined as unrealistic are only reduced instead of eliminated.…”