Decision Forest: A Nonparametric Approach to Modeling Irrational Choice

Abstract

Customer behavior is often assumed to follow weak rationality, which implies that adding a product to an assortment will not increase the choice probability of another product in that assortment. However, an increasing amount of research has revealed that customers are not necessarily rational when making decisions. In this paper, we study a new nonparametric choice model that relaxes this assumption and can model a wider range of customer behavior, such as decoy effects between products. In this model, each customer type is associated with a binary decision tree, which represents a decision process for making a purchase based on checking for the existence of specific products in the assortment. Together with a probability distribution over customer types, we show that the resulting model -a decision forest -is able to represent any customer choice model, including models that are inconsistent with weak rationality. We theoretically characterize the depth of the forest needed to fit a data set of historical assortments and prove that asymptotically, a forest whose depth scales logarithmically in the number of assortments is sufficient to fit most data sets. We also propose an efficient algorithm for estimating such models from data, based on combining randomization and optimization. Using synthetic data and real transaction data exhibiting non-rational behavior, we show that the model outperforms the multinomial logit and ranking-based models in out-of-sample predictive ability.

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

“…A recent working paper by Chen and Mišić (2019) has independently reached a similar conclusion, showing by construction that any choice model can be represented by a decision forest where each of the trees has depth N + 1. While their proof has the virtue of being constructive, we believe that our proof is more succinct and insightful as it shows that the two classes DCMs and BCFs are equivalent.…”

“…For example, there is empirical evidence showing that behavioral considerations of consumers may distort their choice and thus violate regularity, e.g., the decoy e ect (Ariely, 2008) and the comparison-based DCM (Huber et al, 1982;Russo and Dosher, 1983). It is already documented in Chen and Mišić (2019) that the decision forest can capture the decoy e ect. In this section, we use the choice forest to model consumer search.…”

“…A recent paper by Chen and Mišić (2019) proposes a similar tree-based DCM. They show that their "decision forest" can approximate any DCMs with arbitrary precision; a similar result is proved with a di erent approach in this paper.…”

“…They show that their "decision forest" can approximate any DCMs with arbitrary precision; a similar result is proved with a di erent approach in this paper. Although the resulting DCM has a similar structure, our studies di er substantially in the estimation step: we focus on random forests, while Chen and Mišić (2019) follow an optimization approach based on column generation ideas for estimation. Moreover, we establish the consistency of random forests, and show that the estimation can accommodate the price information and aggregate choice data.…”

Data‐driven research in retail operations—A review

“…Chen and Mišić (2019) propose a novel nonparametric approach for customer choice modeling using decision trees. In their proposed model, each customer type is associated with a binary decision tree, which represents a customer's decision given specific offered assortments.…”