北京航空航天大学学报 ›› 2009, Vol. 35 ›› Issue (12): 1443-1445.

• 论文 • 上一篇    下一篇

基于Gumbel Copula函数的多维Logit模型

李华民, 黄海军, 王惠文   

  1. 北京航空航天大学 经济管理学院, 北京 100191
  • 收稿日期:2008-11-21 出版日期:2009-12-31 发布日期:2010-09-14
  • 作者简介:李华民(1979-),男,河南平顶山人,博士生,li_lhm@sohu.com.
  • 基金资助:

    国家自然科学基金资助项目(70521001); 国家973基础研究计划资助项目(2006CB705503)

Multinomial Logit model based on Gumbel Copula

Li Huamin, Huang Haijun, Wang Huiwen   

  1. School of Economics and Management, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
  • Received:2008-11-21 Online:2009-12-31 Published:2010-09-14

摘要: 针对多维Logit模型中的独立同分布(IID, Identically & Independently Distributed)条件假设,提出了一种基于Copula函数的离散选择模型.利用Copula函数获得多元随机变量的联合分布函数以及Gumbel Copula函数的特性,得到了任意2个随机项之差的联合分布,它依然服从Logistic分布,形式上只比现有的分布函数多了一个倍参数.进一步将此结果推广至多维选择问题,得到了无需IID条件下一个方案被选中的概率,从而克服了多维Logit模型的应用障碍.

Abstract: 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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