Abstract
A semi-nonparametric generalized multinomial logit model, formulated using orthonormal Legendre polynomials to extend the standard Gumbel distribution, is presented in this paper. The resulting semi-nonparametric function can represent a probability density function for a large family of multimodal distributions. The model has a closed-form log-likelihood function that facilitates model estimation. The proposed method is applied to model commute mode choice among four alternatives (auto, transit, bicycle and walk) using travel behavior data from Argau, Switzerland. Comparisons between the multinomial logit model and the proposed semi-nonparametric model show that violations of the standard Gumbel distribution assumption lead to considerable inconsistency in parameter estimates and model inferences.
Highlights
IntroductionThe Gumbel distribution ( referred to as the Type-I extreme value distribution) plays a central role in discrete choice models for travel demand analysis[1]
The Gumbel distribution plays a central role in discrete choice models for travel demand analysis[1]
A semi-nonparametric generalized multinomial logit (SGMNL) model is formulated and developed by applying orthonormal Legendre polynomials to extend the standard Gumbel distribution that lies at the core of multinomial logit models applied in practice
Summary
The Gumbel distribution ( referred to as the Type-I extreme value distribution) plays a central role in discrete choice models for travel demand analysis[1]. This can be attributed to two major reasons. With a closed-form likelihood function, maximum likelihood estimation (MLE) methods can be applied with ease to estimate model coefficients consistently and efficiently Due to these appealing features of the Gumbel distribution, the Multinomial Logit (MNL) model is widely applied in practice and preferred over its counterpart that is based on the assumption of a normally distributed random error component (i.e., Multinomial Probit or MNP model)[2,3,4]. In the context of discrete-continuous choice behaviors, the Multiple Discrete-Continuous Extreme Value (MDCEV) model[5,6,7,8,9] developed based on the standard
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