  This paper analyzes consumer choices over lunchtime restaurants using data
from a sample of several thousand anonymous mobile phone users in the San
Francisco Bay Area. The data is used to identify users' approximate typical
morning location, as well as their choices of lunchtime restaurants. We build a
model where restaurants have latent characteristics (whose distribution may
depend on restaurant observables, such as star ratings, food category, and
price range), each user has preferences for these latent characteristics, and
these preferences are heterogeneous across users. Similarly, each item has
latent characteristics that describe users' willingness to travel to the
restaurant, and each user has individual-specific preferences for those latent
characteristics. Thus, both users' willingness to travel and their base utility
for each restaurant vary across user-restaurant pairs. We use a Bayesian
approach to estimation. To make the estimation computationally feasible, we
rely on variational inference to approximate the posterior distribution, as
well as stochastic gradient descent as a computational approach. Our model
performs better than more standard competing models such as multinomial logit
and nested logit models, in part due to the personalization of the estimates.
We analyze how consumers re-allocate their demand after a restaurant closes to
nearby restaurants versus more distant restaurants with similar
characteristics, and we compare our predictions to actual outcomes. Finally, we
show how the model can be used to analyze counterfactual questions such as what
type of restaurant would attract the most consumers in a given location.

Econometrics;Artificial Intelligence;Applications;Machine Learning