Sampling of alternatives for route choice modeling
Transportation Research Part B: Methodological
Recently, we proposed a new paradigm for choice set generation in the context of route choice model estimation. As detailed in Frejinger and Bierlaire (2007) , we assume that choice sets contain all paths connecting each origin-destination pair. Although it is behaviorally questionable, this assumption is made in order to avoid bias in the econometric model. These sets are in general impossible to generate explicitly. Therefore, we propose an importance sampling approach to generate subsets of
... aths suitable for model estimation. Using only a subset of alternatives requires the path utilities to be corrected according to the sampling protocol in order to obtain unbiased parameter estimates. In Frejinger and Bierlaire (2007) we derive such a sampling correction for the multinomial logit (MNL) model. The path size logit model is a MNL model where a path size (PS) attribute is included in the deterministic utilities. The PS attribute should capture the correlation among routes. It is generally computed based on sampled paths only but we argue that it should capture the correlation among all routes (universal choice set). This becomes problematic since the universal choice set is unknown in practice. In this paper we present a generalization of the PS attribute called expanded PS (EPS). It is computed based on sampled paths only but involves an expansion factor that corrects for the sampling. We present estimation results based on synthetic data that clearly show the strength of this approach. Unbiased parameter estimates are only obtained for models including a sampling correction. Moreover, the results show that EPS is superior to the original PS attribute.