4.36 Mixed MNL Models for Discrete Response

This paper considers mixed, or random coefficients, multinomial logit
(MMNL) models for discrete response, and establishes the following
results: Under mild regularity conditions, any discrete choice model
derived from random utility maximization has choice probabilities that
can be approximated as closely as one pleases by an MMNL
model. Practical estimation of a parametric mixing family can be
carried out by Maximum Simulated Likelihood Estimation. Nonparametric
estimation of a random utility model for choice can be approached by
successive approximations by MMNL models with finite mixing
distributions; e.g., latent class models. A mixed MNL model with
normally distributed coefficients can approximate a multinomial probit
model. The adequacy of a mixing specification can be tested simply as
an omitted variable test with appropriately defined artificial
variables. An application to a problem of d for alternative vehicles
shows that MMNL provides a flexible and computationally practical
approach to discrete response analysis.