Summed-probability logit models

The note presents and discusses summed-probability logit choice models, by which is meant models giving the probability of the observed choice as the sum of a number of probabilities given by a tree-nested logit model. The ways in which these models can be used to represent indeterminate choice, cross-nested and latent class models are explained and the advantages of the summed-probability representation are demonstrated, as well as the extension to multiple levels and the way in which the treatment of ‘size’ variables is simplified. Formulae for model estimation are also given. The summed-probability representation gives insight into a general family of logit models and is expected to help analysts make efficient estimations of a variety of specifications. • Consistent formulae for indeterminate choice, cross-nested logit and latent class models. • Straightforward treatment of size variables and allocation parameters in CNL. • First and second derivatives for these model types.