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The Recurrent Problem of Parametrising Nested Logit Models

This paper describes how nested logit models are widely used for travel demand analysis, mainly using tree structures but occasionally generalizing these to allow cross-nesting. An important part of the justification for these models is that they can be derived from a theory of individual utility maximization, although other theoretical bases also exist. This justification gives the models the familiar Random Utility (RU) basis by exploiting the concept of error in the utility function. The nested logit model allows asymmetry among the alternatives even at an individual level, thus avoiding reliance on an assumption of independence from irrelevant alternatives. This generalization is obtained by introducing additional parameters into the structure that express the ratio of the standard errors of utility between alternatives in different subsets. However, there is no unique way to parametrize these ratios. Different parametrizations have existed since the models were originally shown to be consistent with RU but these were frequently ignored or overlooked. More recently, a series of papers have identified two main parametrizations, called RU1 and RU2, not very originally, and have indicated some of the main issues. However, some of these papers contain important errors and there are further difficulties in ensuring consistency with RU in practical contexts. This paper presents the issues and the RU1 and RU2 parametrizations. The way in which RU tests apply to these is explained, along with the conclusion, not made explicit in the literature, that RU2 is always RU-consistent but that RU1 may require constraints or extensions to the model to make it so. The tests that have been applied to the models involve hypothetical changes to the (indirect) conditional utility of choosing each alternative. This does not help much in practice, of course, because there is a need to work with measurable variables, such as time and cost. But these variables raise further issues when they are included in the model in non-linear form and these issues are still the subject of research. The issues will be discussed briefly. Finally, the paper discusses a further issue of normalization that arises in cross-nested models, where the allocation parameters that specify the way in which the cross-nesting operates require constraint, but the literature is again inconsistent. An effective normalization is proposed and explained. It is hoped that the paper will reduce the uncertainty and confusion surrounding this issue which persist despite the efforts that have been made to reduce them.

Language

  • English

Media Info

  • Media Type: Digital/other
  • Pagination: v.p.
  • Monograph Title: European Transport Conference, 2010 Proceedings

Subject/Index Terms

Filing Info

  • Accession Number: 01353836
  • Record Type: Publication
  • Files: TRIS
  • Created Date: Oct 19 2011 12:52PM