Estimating Large-Scale Tree Logit Models via a Difference of Strictly Convex Functions

63 Pages Posted: 10 Jul 2019

See all articles by Srikanth Jagabathula

Srikanth Jagabathula

New York University (NYU) - Department of Information, Operations, and Management Sciences

Paat Rusmevichientong

University of Southern California - Marshall School of Business

Date Written: August 26, 2018

Abstract

We describe an efficient estimation method for large-scale tree logit models, using a novel change-of-variables transformation that allows us to express the negative log-likelihood as a difference of strictly convex functions. Exploiting this representation, we design a fast iterative method that computes a sequence of parameter estimates. At each iteration, parameters at leaf nodes are updated using a simple formula involving the Lambert-W function, while the parameters at non-leaf nodes are updated simultaneously by minimizing a strictly convex one-dimensional function over the unit interval. No step size or second-order derivative is required. The sequence of parameter estimates yields increasing likelihood values, and we show that every limit point is a stationary point. Numerical results show that our algorithm outperforms state-of-the-art optimization methods, especially for large-scale tree logit models with thousands of nodes.

Keywords: tree logit, choice modeling, parameter estimation

Suggested Citation

Jagabathula, Srikanth and Rusmevichientong, Paat, Estimating Large-Scale Tree Logit Models via a Difference of Strictly Convex Functions (August 26, 2018). NYU Stern School of Business. Available at SSRN: https://ssrn.com/abstract=3416311 or http://dx.doi.org/10.2139/ssrn.3416311

Srikanth Jagabathula (Contact Author)

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

Paat Rusmevichientong

University of Southern California - Marshall School of Business ( email )

701 Exposition Blvd
Los Angeles, CA 90089
United States

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