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Cost damping and functional form in transport models

机译：运输模型中的成本衰减和功能形式

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Transport models allowing for cost damping are characterised by marginally decreasing cost sensitivities in demand. As a result, cost damping is a model extension of the simple linear-in-cost model requiring an appropriate non-linear link function between utility and cost. The link function may take different forms and be represented as a non-linear-in-parameter form such as the well-known Box-Cox function. However, it could also be specified as non-linear-in-cost but linear-in-parameter forms, which are easier to estimate and improve model fit without increasing the number of parameters. The specific contributions of the paper are as follows. Firstly, we discuss the phenomenon of cost damping in details and specifically why it occurs. Secondly, we provide a test of damping and an easy assessment of the (linear) damping rate for any variable by estimating two auxiliary linear models. This turns out to be an important guidance as the damping rate largely dictates which link functions are appropriate for the data. Thirdly, inspired by the Box-Cox function, we propose alternative linear-in-parameter link functions, some of which are based on interpolation of approximate Box-Cox end points, and others which are inspired by Taylor Expansions. The different functions are tested in simulation experiments and subsequently in a large-scale demand model based on more than 22,000 revealed preference observations. It is concluded that the use of properly specified linear-in-parameter functions gives good data fit and sometimes even outperforms the Box-Cox functions without increasing the number of parameters.
机译：允许降低成本的运输模型的特征在于，需求的成本敏感性略有降低。结果，成本衰减是简单的成本成本线性模型的模型扩展，需要效用和成本之间适当的非线性链接函数。链接函数可以采用不同的形式，并表示为非线性参数形式，例如众所周知的Box-Cox函数。但是，也可以将其指定为成本成本非线性但参数线性的形式，在不增加参数数量的情况下，更易于估计和改进模型拟合。本文的具体贡献如下。首先，我们详细讨论成本衰减现象，特别是它发生的原因。其次，我们通过估计两个辅助线性模型来提供阻尼测试和对任何变量的（线性）阻尼率的轻松评估。事实证明，这是一个重要的指导，因为阻尼率在很大程度上决定了哪些链接功能适合于数据。第三，受Box-Cox函数启发，我们提出了替代的线性参数链接函数，其中一些基于近似Box-Cox端点的插值，而另一些则基于Taylor Expansions。在仿真实验中测试了不同的功能，随后在基于超过22,000个揭示的偏好观察的大规模需求模型中进行了测试。结论是，使用正确指定的参数线性输入函数可提供良好的数据拟合，并且有时甚至在不增加参数数量的情况下优于Box-Cox函数。

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