Mixed Logit with Bounded Distributions of Correlated Partworths

Abstract

The use of a joint normal distribution for partworths is computationally attractive, particularly with Bayesian MCMC procedures, and yet is unrealistic for any attribute whose partworth is logically bounded (e.g., is necessarily positive or cannot be unboundedly large). A mixed logit is specified with partworths that are transformations of normally distributed terms, where the transformation induces bounds; examples include censored normals, log-normals, and S _B distributions which are bounded on both sides. The model retains the computational advantages of joint normals while providing greater flexibility for the distributions of correlated partworths. The method is applied to data on customers’ choice among vehicles in stated choice experiments. The flexibility that the transformations allow is found to greatly improve the model, both in terms of fit and plausibility, without appreciably increasing the computational burden.

A Gauss routine and manual to implement the procedures described in this paper are available on Train’s website at http:\\elsa.berkeley.edu\~train. We are grateful for comments from Peter Rossi on an earlier version of this paper.