Improved Estimation of Flexible Logit Models and an Extension to a Model with a t-distributed Error Kernel

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Understanding various micro-decisions of travelers (e.g., choice of vehicles, travel modes, or destinations) is of utmost importance in travel demand modeling. After the first application of the multinomial logit model in the early 1970s, micro-econometric models to elicit these type of choices have evolved in mainly two ways: a) computationally efficient estimation (e.g., fast integral approximations); and b) behaviorally defensible models (e.g., modeling preference heterogeneity). This dissertation contributes to both lines of behavior modeling research -- whereas chapters one to three analyze and improve the computational efficiency of flexible logit models and the required approximation of high-dimensional integrals, chapter four derives the first multinomial response model with a t-distributed error kernel that accounts for decision uncertainty behavior of travelers. A summary of each chapter is provided below. In Chapter 1, we extend the logit-mixed logit (LML) model, an advanced semi-parametric specification of preference heterogeneity, to a combination of fixed and random parameters. We show that the likelihood of the LML specification loses its special properties due to the inclusion of fixed parameters, leading to a much higher estimation time. In an empirical application about preferences for alternative fuel vehicles in China, estimation time increased by a factor of 20-40 when introducing fixed parameters. Despite losses in computation efficiency, we show that the flexible LML could retrieve multimodal mixing distributions. In Chapter 2, we derive, implement, and test minorization-maximization (MM) algorithms to estimate the semiparametric LML and mixture-of-normals multinomial logit (MON-MNL) models. In a Monte Carlo study and empirical application to estimate consumer's willingness to adopt electric motorcycles in Indonesia, we compare the maximum simulated likelihood estimator (MSLE) with the derived MM algorithms. Whereas in LML estimation MM is computationally noncompetitive with MSLE, it is a competitive replacement to MSLE for MON-MNL that obviates computation of complex analytical gradients. In Chapter 3, we propose the application of a moment-based designed quadrature (DQ) method to approximate multi-dimensional integrals in MSLE of discrete choice models. The results of simulation study indicate that DQ is a potentially attractive alternative to quasi-Monte Carlo (QMC) because it requires fewer evaluations of the conditional likelihood (i.e., lower computation time) as compared to QMC methods, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial spaces. Finally, we validate the performance of DQ on a case study to understand preferences for mobility-on-demand services in New York City. In Chapter 4, we demonstrate that using a t-distributed error kernel in multinomial choice models helps in better predicting the preferences in class-imbalance datasets. This specification also implicitly accounts for the consumers' decision uncertainty behavior. Because of these statistical and behavioral advantages, we derive the first multinomial response model with a t-distributed error kernel and extend this to a generalized continuous-multinomial (GCM) model. In the empirical study related to the adoption of electric vehicles (EVs), we observe that accounting for decision uncertainty behavior in the GCM model with t-distributed error kernel results into a higher willingness to pay for improving the EV attributes than those of a GCM model with a normally-distributed error kernel. These differences are relevant in making policies to expedite the market penetration of EVs.
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Discrete choice models; Integral approximation; Minorization-maximization algorithm; Semiparametric logit models; T-distributed kernel; Economics; Willingness to Pay; Transportation; Statistics
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Alvarez Daziano, Ricardo
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Diciccio, Thomas J.
Li, Shanjun
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Civil and Environmental Engineering
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Ph.D., Civil and Environmental Engineering
Degree Level
Doctor of Philosophy
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