Alternative tree logit models: comments on a paper of Koppelman and Wen

The paper by Koppelman and Wen (1998) on nested logit structures (subsequently referred to as K&W), draws attention to alternative formulations of nested or 'tree' logit models. The intention of this note is to highlight some deficiencies in that paper and comment on the points raised in the discussion. The alternative model forms in question are stated concisely and generally and some properties of each form are derived. Then the consistency of model forms with the theory of utility maximisation and the relationship between alternative formulations are discussed. Finally, the appropriate advice for practitioners is discussed.