Specification and Estimation of Nested Logit Models

Abstract

The nested logit model is currently the preferred extension to the simple
\nmultinomial logit discrete choice model. The appeal of the nested logit
\nmodel is its ability to accommodate differential degrees of
\ninterdependence (i.e. similarity) between subsets of alternatives in a
\nchoice set. The received literature displays a frequent lack of attention
\nto the very precise form that a nested logit model must take to ensure
\nthat the resulting model is invariant to normalisation of scale and is
\nconsistent with utility maximisation. Some recent papers by
\nKoppelman and Wen (1998a, 1998b) and Hunt (1998) have addressed
\nsome aspects of this issue, but some important points remain somewhat
\nambiguous.
\nWhen utility function parameters have different implicit scales,
\nimposing equality restrictions on common attributes associated with
\ndifferent alternatives (i.e. making them generic) can distort these
\ndifferences in scale. Model scale parameters are then ‘forced’ to take
\nup the real differences that should be handled via the utility function
\nparameters. With many variations in model specification appearing in
\nthe literature, comparisons become difficult, if not impossible, without
\nclear statements of the precise form of the nested logit model. There
\nare a number of approaches to achieving this, with some or all of them
\navailable as options in commercially available software packages.
\nThis note seeks to clarify the issue, and to establish the points of
\nsimilarity and dissimilarity of the different formulations that appear in
\nthe literature.

Keywords

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