Discrete Choice Analysis with Machine Learning Capabilities

This paper discusses capabilities that are essential to models applied in policy analysis settings and the limitations of direct applications of off-the-shelf machine learning methodologies to such settings. Traditional econometric methodologies for building discrete choice models for policy analysis involve combining data with modeling assumptions guided by subject-matter considerations. Such considerations are typically most useful in specifying the systematic component of random utility discrete choice models but are typically of limited aid in determining the form of the random component. We identify an area where machine learning paradigms can be leveraged, namely in specifying and systematically selecting the best specification of the random component of the utility equations. We review two recent novel applications where mixed-integer optimization and cross-validation are used to algorithmically select optimal specifications for the random utility components of nested logit and logit mixture models subject to interpretability constraints.

Sparse Covariance Estimation in Logit Mixture Models

This paper introduces a new data-driven methodology for estimating sparse covariance matrices of the random coefficients in logit mixture models. Researchers typically specify covariance matrices in logit mixture models under one of two extreme assumptions: either an unrestricted full covariance matrix (allowing correlations between all random coefficients), or a restricted diagonal matrix (allowing no correlations at all). Our objective is to find optimal subsets of correlated coefficients for which we estimate covariances. We propose a new estimator, called MISC, that uses a mixed-integer optimization (MIO) program to find an optimal block diagonal structure specification for the covariance matrix, corresponding to subsets of correlated coefficients, for any desired sparsity level using Markov Chain Monte Carlo (MCMC) posterior draws from the unrestricted full covariance matrix. The optimal sparsity level of the covariance matrix is determined using out-of-sample validation. We demonstrate the ability of MISC to correctly recover the true covariance structure from synthetic data. In an empirical illustration using a stated preference survey on modes of transportation, we use MISC to obtain a sparse covariance matrix indicating how preferences for attributes are related to one another.