hundreds of thousands of iterations. These difficulties are well known. MCMC is rarely applied to large-scale heterogeneous models. Indeed, to address scalability, it is common to work with data from a subset of individuals, or a subset of choice items. However, this approach discards information that is valuable in the inferential process, and it can lead to biased estimates (Bradlow and Zanutto 2006). In this paper, we derive variational algorithms for a common discrete choice model – the mixed multinomial logit (MML) model. We study this model because it the workhorse of discrete choice theory and is well known in many disciplines, including economics and marketing. There are other popular discrete choice models in the literature, but the mixed multinomial logit has appeal: it is conceptually simple, yet still exhibits the MCMC infer- ence issues just described. The rest of the paper is organized as follows. Section 2 presents the details of the MML model. In Section 3, we describe variational procedures suitable for empirical Bayes and fully Bayesian inference under the MML model. These procedures include a novel application of the delta method for moments to variational inference. In Section 4, we compare variational methods to MCMC for the MML model, using an extensive suite of simulated data sets. Section 5 closes with discussion and future directions. Technical arguments and derivations are relegated to Appendixes A, B, and C. Let there be H agents, indexed h D 1 ; : : : ; H . We observe a total of T$_{h}$ choice-event outcomes for agent h . At each choice event, the agent selects from among a fixed set of J items, indexed j D 1 ; : : : ; J . The items are differentiated according to K attributes, indexed k D 1 ; : : : ; K . The j th item’s value for the k th attribute can vary across agents and from one choice event to another. For example, households might shop at different stores charging various prices for the same good, and the price of a good may change over 4 2 The mixed multinomial logit model of discrete choice