Volume 35 Issue 12
Dec.  2009
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Li Huamin, Huang Haijun, Wang Huiwenet al. Multinomial Logit model based on Gumbel Copula[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(12): 1443-1445. (in Chinese)
Citation: Li Huamin, Huang Haijun, Wang Huiwenet al. Multinomial Logit model based on Gumbel Copula[J]. Journal of Beijing University of Aeronautics and Astronautics, 2009, 35(12): 1443-1445. (in Chinese)

Multinomial Logit model based on Gumbel Copula

  • Received Date: 21 Nov 2008
  • Publish Date: 31 Dec 2009
  • For the IID(identically & independently distributed) condition of the multinomial Logit model, which requires all random terms existing in the utilities of alternatives to be independent each other, a discrete choice model was proposed, based on the Copula function which can be used to derive the joint probability distribution of multi-random variables. The IID condition is weakened and the distribution of the difference between every two random terms is obtained using the Gumbel Copula function-s property. It is found that this distribution still follows the Logistic type but the difference must be multiplied by a parameter which can be estimated by the likelihood method from survey data. This result is then extended and employed in the discrete choice problem with more than two alternatives. The probability of choosing a specific alternative is rigorously formulated. The work surmounts the difficulty of applying the multinomial Logit model.

     

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  • [1] McFadden D. Modeling the choice of residential location Karlqvist A,Snickars F,Weibull J.Spatial Interaction Theory and Planning Models.Amsterdam:North-Holland,1978:105-142 [2] 关宏志.非集计模型:交通行为分析的工具[M].北京:人民交通出版社,2004 Guan Hongzhi.Disaggregate mode:a tool of traffic behavior analysis[M].Beijing: China Communications Press,2004(in Chinese) [3] McFadden D,Train K E.Mixed MNL models of discrete response [J].Journal of Applied Econometrics,2000,15(5):447-470 [4] Hess S,Bierlaire M.Estimation of value of travel-time savings using mixed logit models [J].Transportation Research Part A,2005,39(3): 221-236 [5] Greene W H,Hensher D A.Accounting for heterogeneity in the variance of unobserved effects in mixed logit models [J].Transportation Research Part B,2006,40(1):75-92 [6] 陆化普,黄海军.交通规划理论研究前沿 [M].北京:清华大学出版社,2007:77-91 Lu Huapu,Huang Haijun.Theory research progress of transportation planning [M].Beijing: Tsinghua University Press,2007:77-91(in Chinese) [7] Train K E.Discrete choice methods with simulation[M].UK: Cambridge University Press,2003 [8] Nelsen R B.An introduction to Copulas[M].Second Edition.New York: Springer Verlag,2006 [9] Genest C,Rivest L P.A characterization of Gumbel-s family of extreme value distributions [J].Statist Probab Lett,1989,8(3): 207-211 [10] Hutchinson T P,Lai C D.Continuous bivariate distributions,emphasising applications [M].Adelaide: Rumsby Scientific Publishing,1990 [11] Joe H,Xu J J.The estimation method of inference functions for margins for multivariate models .Department of Statistics,University of British Columbia,Technical Report,166,1996 [12] 杨振海,程维虎.基于Logistic总体Ⅱ型截尾样本分布参数的近似极大似然估计[J].北京工业大学学报,2004,30(2):235-240 Yang Zhenhai,Cheng Weihu.Approximate maximum likelihood estimation based on Logistic distribution parameters of type Ⅱ censored samples [J].Journal of Beijing Polytechnic University,2004,30(2):235-240 (in Chinese)
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