Specification and estimation of the nested logit model: alternative normalisations

Abstract

The nested logit model is currently the preferred extension to the simple multinomial logit (MNL) discrete choice model. The appeal of the nested logit model is its ability to accommodate differential degrees of interdependence (i.e., similarity) between subsets of alternatives in a choice set. The received literature displays a frequent lack of attention to the very precise form that a nested logit model must take to ensure that the resulting model is invariant to normalisation of scale and is consistent with utility maximisation. Some recent papers by F.S. Koppelman, C.H. Wen [Transp. Res. B 32 (5) (1998a) 289; Transp. Res. Record 1645 (1998b) 1] and G.L. Hunt [Nested logit models with partial degeneracy, Department of Economics, University of Maine, December 1998 (revised)] have addressed some aspects of this issue, but some important points remain somewhat ambiguous. When utility function parameters have different implicit scales, imposing equality restrictions on common attributes associated with different alternatives (i.e., making them generic) can distort these differences in scale. Model scale parameters are then ‘forced’ to take up the real differences that should be handled via the utility function parameters. With many variations in model specification appearing in the literature, comparisons become difficult, if not impossible, without clear statements of the precise form of the nested logit model. There are a number of approaches to achieving this, with some or all of them available as options in commercially available software packages. This article seeks to clarify the issue, and to establish the points of similarity and dissimilarity of the different formulations that appear in the literature.