A practically tractable expression of the covariances of the Cross-Nested Logit model
A practically tractable expression of the covariances of the Cross-Nested Logit model
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交叉嵌套 Logit 模型协方差的实用易处理表达式
DOI：
10.1016/j.trb.2013.08.017
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发表时间：
2013
影响因子：
6.8
通讯作者：
R. Vitillo
中科院分区：
文献类型：
--
作者：
V. Marzano;A. Papola;F. Simonelli;R. Vitillo
本文提出了一种实用的数学方法，用于计算任何给定的交叉嵌套Logit（CNL）模型下的协方差，基于一维随机变量的方差，其累积分布函数和密度概率函数以封闭形式给出。这允许将CNL协方差表示为仅一维积分的函数，可以通过标准数值技术轻松有效地进行评估，也可以在基本的计算机电子表格中实现。首先，一个正式的理论证明的过程进行了说明。然后，与Marzano和Papola [Marzano，V.，帕波拉，2008.交叉嵌套Logit模型的协方差结构。运输研究B 42（2），83-98]，并讨论了有关该程序的实际执行细节。最后，估计的CNL模型的背景下与先前的期望的协方差/相关性实际解决，由于CNL协方差的计算中实现的简化。
This paper proposes a practically tractable mathematical procedure for the calculation of the covariances underlying whatever given Cross-Nested Logit (CNL) model, based on the variance of a one-dimensional random variable, whose cumulative distribution function and density probability function are given in closed form. This allows expressing the CNL covariances as a function of just a one-dimensional integral, which can be evaluated easily and effectively by means of standard numerical techniques, implementable also in basic computer spreadsheets. Firstly, a formal theoretical proof of the procedure is illustrated. Then, a comparison with the calculations performed by Marzano and Papola [Marzano, V., Papola, ., 2008. On the covariance structure of the Cross-Nested Logit model. Transportation Research B 42(2), 83–98] is proposed, and details about the practical implementation of the procedure are discussed. Finally, estimation of the CNL model in contexts with prior expectations on covariances/correlations is addressed practically, thanks to the simplification achieved in the calculation of the CNL covariances.