Abstract
A new approach for estimating the aggregate hierarchical logit model is presented. Though usually derived from random utility theory assuming correlated stochastic errors, the model can also be derived as a solution to a maximum entropy problem. Under the latter approach, the Lagrange multipliers of the optimization problem can be understood as parameter estimators of the model. Based on theoretical analysis and Monte Carlo simulations of a transportation demand model, it is demonstrated that the maximum entropy estimators have statistical properties that are superior to classical maximum likelihood estimators, particularly for small or medium-size samples. The simulations also generated reduced bias in the estimates of the subjective value of time and consumer surplus.
Highlights
In urban transportation planning, travel demand is frequently represented by multinomial or hierarchical logit discrete choice models, for the selection of destinations, routes, and transportation modes
The conclusions are similar for the two cases, but with φ = 1/μ = 0.9 it is especially clear that the Maximum Likelihood (ML) estimate for the Hierarchical Logit (HL) model reproduces the modal shares must more accurately. This result is to be expected given that a value for the parameter φ closer to 1 implies that the HL model is more similar to an multinomial logit (MNL) one, which always reproduces the observed modal shares when estimated with ML
In the context of aggregate transportation demand forecasting and land use planning, entropy maximization problems are often formulated, mainly because their solutions are the well-known multinomial logit and hierarchical logit models. The parameters of these models are normally estimated using the maximum likelihood method, but they can be estimated by solving the entropy maximization problems directly
Summary
Travel demand is frequently represented by multinomial or hierarchical logit discrete choice models, for the selection of destinations, routes, and transportation modes. These models are used in land use planning for modeling the real estate supply and activity location. The endogenous and exogenous parameters of these models are estimated by applying certain statistical techniques used for calibrating econometric models, most notably the maximum likelihood method This is a sensible strategy for a multinomial logit model given the equivalence of the two estimators noted above, but may not be the best option if the model is hierarchical logit. Our conclusion is that the maximum entropy estimators provide a viable alternative for estimating hierarchical logit models; in the light of the simulations they appear to be superior to maximum likelihood estimates, especially with small sample sizes
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