Frejinger, E., and Bierlaire, M. (2007)
Capturing correlation with subnetworks in route choice models, Transportation Research Part B: Methodological 41(3):363-378.
When using random utility models for a route choice problem, a critical issue is the significant correlation among alternatives. There are basically two types of models proposed in the literature to address it: (i) a deterministic correction of the path utilities in a Multinomial Logit model (such as the Path Size Logit or the C-Logit models) and (ii) an explicit modeling of the correlation through assumptions about the error terms, and the use of advanced discrete choice models such as the Cross-Nested Logit or the Error Component models. The first is simple, easy to handle and often used in practice. Unfortunately, it does not correctly capture the correlation structure, as we discuss in details in the paper. The second is more consistent with the modeling objectives, but very complicated to specify and estimate. The modeling framework proposed in this paper allows the analyst to control the trade-off between the simplicity of the model and the level of realism. Within this framework, the key concept capturing the correlation structure is called a subnetwork. A subnetwork is a simplification of the road network only containing easy identifiable and behaviorally relevant roads. In practice, the subnetwork can easily be defined based on the route network hierarchy. The importance and the originality of our approach lie in the possibility to capture the most important correlation without considerably increasing the model complexity. This makes it suitable for a wide spectrum of applications, namely involving realistic large-scale networks. As an illustration, we present estimation results of a factor analytic specification of a mixture of Multinomial Logit model, where the correlation among paths is captured by error components. The estimation is based on a GPS dataset collected in the Swedish city of Borlänge. The results show a significant increase in model fit and forecasting performance for the Error Component model compared to a Path Size Logit model. Moreover, the correlation parameters are significant.
doi:10.1016/j.trb.2006.06.003 (click here for the full paper)