Wang Ke, Ye Xin, Pendyala Ram M, Zou Yajie
Key Laboratory of Road and Traffic Engineering of Ministry of Education, College of Transportation Engineering, Tongji University, Shanghai, China.
School of Sustainable Engineering and the Built Environment, Arizona State University, Tempe, Arizona, United States of America.
PLoS One. 2017 Oct 26;12(10):e0186689. doi: 10.1371/journal.pone.0186689. eCollection 2017.
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.
本文提出了一种半非参数广义多项logit模型，该模型使用正交勒让德多项式来扩展标准耿贝尔分布。由此产生的半非参数函数可以表示一大类多峰分布的概率密度函数。该模型具有便于模型估计的闭式对数似然函数。所提出的方法应用于使用来自瑞士阿尔高州的出行行为数据对四种出行方式（汽车、公共交通、自行车和步行）的通勤方式选择进行建模。多项logit模型与所提出的半非参数模型之间的比较表明，违反标准耿贝尔分布假设会导致参数估计和模型推断出现相当大的不一致。
