[Paper Review] Machine Learning Meets Microeconomics: The Case of Decision Trees and Discrete Choice

Timothy Brathwaite, Akshay Vij+1 more|arXiv (Cornell University)|Nov 13, 2017

Economic and Environmental Valuation20 citations

TL;DR

This paper introduces a Bayesian model tree that integrates decision trees with discrete choice theory, framing decision trees as non-compensatory disjunctions-of-conjunctions rules and embedding them within a two-stage semi-compensatory model. It demonstrates that the Bayesian model tree outperforms the multinomial logit model by over 1,000 times in approximating the true data-generating process in a bicycle mode choice study, capturing diminishing returns on bike infrastructure and context-dependent behavioral heterogeneity.

ABSTRACT

We provide a microeconomic framework for decision trees: a popular machine learning method. Specifically, we show how decision trees represent a non-compensatory decision protocol known as disjunctions-of-conjunctions and how this protocol generalizes many of the non-compensatory rules used in the discrete choice literature so far. Additionally, we show how existing decision tree variants address many economic concerns that choice modelers might have. Beyond theoretical interpretations, we contribute to the existing literature of two-stage, semi-compensatory modeling and to the existing decision tree literature. In particular, we formulate the first bayesian model tree, thereby allowing for uncertainty in the estimated non-compensatory rules as well as for context-dependent preference heterogeneity in one's second-stage choice model. Using an application of bicycle mode choice in the San Francisco Bay Area, we estimate our bayesian model tree, and we find that it is over 1,000 times more likely to be closer to the true data-generating process than a multinomial logit model (MNL). Qualitatively, our bayesian model tree automatically finds the effect of bicycle infrastructure investment to be moderated by travel distance, socio-demographics and topography, and our model identifies diminishing returns from bike lane investments. These qualitative differences lead to bayesian model tree forecasts that directly align with the observed bicycle mode shares in regions with abundant bicycle infrastructure such as Davis, CA and the Netherlands. In comparison, MNL's forecasts are overly optimistic.

Motivation & Objective

• To bridge the gap between machine learning and microeconomics by providing an economic interpretation of decision trees.
• To address the reluctance of discrete choice modelers to adopt machine learning methods due to lack of theoretical grounding.
• To develop a semi-compensatory, two-stage model that combines non-compensatory decision rules with compensatory choice modeling.
• To quantify uncertainty in non-compensatory rules and preference heterogeneity using a Bayesian framework.
• To empirically validate the model using bicycle mode choice data from the San Francisco Bay Area.

Proposed method

• Models decision trees as a non-compensatory decision protocol called disjunctions-of-conjunctions, representing rules like 'if (bicycle lane > 30%) or (travel distance < 2 km), then consider biking'.
• Proposes a two-stage decision process: first, a decision tree defines a choice set based on non-compensatory rules; second, a compensatory discrete choice model (e.g., MNL) selects among alternatives in the set.
• Develops the first Bayesian model tree, allowing uncertainty quantification over both the non-compensatory rules and the parameters of the choice model.
• Uses Markov Chain Monte Carlo (MCMC) methods to estimate the posterior distribution over decision tree structures and choice model parameters.
• Incorporates context-dependent preference heterogeneity by allowing tree splits and choice model parameters to vary by individual-level covariates.
• Employs a hierarchical prior structure to model uncertainty in the non-compensatory rules and to regularize model complexity.

Experimental results

Research questions

• RQ1 How can decision trees be interpreted through the lens of microeconomic decision theory?
• RQ2 Can a two-stage, semi-compensatory model combining decision trees and discrete choice models improve predictive accuracy and policy relevance?
• RQ3 How does uncertainty in non-compensatory rules affect forecast reliability and model robustness?
• RQ4 What behavioral insights does the model reveal that traditional compensatory models like MNL miss?
• RQ5 To what extent does the Bayesian model tree outperform the multinomial logit model in capturing real-world mode choice behavior?

Key findings

• The Bayesian model tree is approximately 1,100 times more likely to be closer to the true data-generating process than the multinomial logit (MNL) model, based on a Bayes factor of 99.01 / 0.09 ≈ 1,100.
• The model forecasts bicycle mode shares accurately in regions with high infrastructure, such as Davis, CA and the Netherlands, whereas the MNL model produces overly optimistic forecasts.
• The model reveals that investments in on-street bicycle lanes exhibit diminishing returns, a key insight absent in the MNL model.
• The model identifies that travel distance, child-related pressures, and topography moderate the effectiveness of bicycle infrastructure, preventing individuals from biking even with high lane availability.
• The Bayesian model tree captures context-dependent preference heterogeneity, showing that non-compensatory rules vary by socio-demographics and environmental conditions.
• The model’s non-compensatory structure ensures that the proportion of bike lanes does not compensate for other variables, fixing β_bike-lanes = 0 and leading to stable forecast uncertainty.