The Use of Binary Choice Forests to Model and Estimate Discrete Choice Models

We show the equivalence of discrete choice models and the class of binary choice forests, which are random forest based on binary choice trees. This suggests that standard machine learning techniques based on random forest can serve to estimate discrete choice model with an interpretable output. This is confirmed by our data driven result that states that random forest can accurately predict the choice probability of any discrete choice model. Our framework has unique advantages: it can capture behavioral patterns such as irrationality or sequential searches; 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. Our numerical results show that binary choice forest can outperform the best parametric models with much better computational times.