  Problem definition. In retailing, discrete choice models (DCMs) are commonly
used to capture the choice behavior of customers when offered an assortment of
products. When estimating DCMs using transaction data, flexible models (such as
machine learning models or nonparametric models) are typically not
interpretable and hard to estimate, while tractable models (such as the
multinomial logit model) tend to misspecify the complex behavior represeted in
the data. Methodology/results. In this study, we use a forest of binary
decision trees to represent DCMs. This approach is based on random forests, a
popular machine learning algorithm. The resulting model is interpretable: the
decision trees can explain the decision-making process of customers during the
purchase. We show that our approach can predict the choice probability of any
DCM consistently and thus never suffers from misspecification. Moreover, our
algorithm predicts assortments unseen in the training data. The mechanism and
errors can be theoretically analyzed. We also prove that the random forest can
recover preference rankings of customers thanks to the splitting criterion such
as the Gini index and information gain ratio. Managerial implications. The
framework has unique practical advantages. It can capture customers' behavioral
patterns such as irrationality or sequential searches when purchasing a
product. It handles nonstandard formats of training data that result from
aggregation. It can measure product importance based on how frequently a random
customer would make decisions depending on the presence of the product. It can
also incorporate price information and customer features. Our numerical
experiments using synthetic and real data show that using random forests to
estimate customer choices can outperform existing methods.
