Estimating Large-Scale Tree Logit Models

87 Pages Posted: 10 Jul 2019 Last revised: 16 Dec 2022

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

Ashwin Venkataraman

Jindal School of Management, UT Dallas

Xinyi Zhao

New York University (NYU) - Leonard N. Stern School of Business

Date Written: November 20, 2022

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 strictly convex function in the leaf node parameters and a difference of strictly convex functions in the non-leaf node parameters. Exploiting this representation, we design a fast iterative method that computes a sequence of parameter estimates using simple closed-form updates. Our algorithm relies only on first-order information (function and gradients values), but unlike other first-order methods, it does not require any step size tuning or costly projection steps. The sequence of parameter estimates yields increasing likelihood values, and we establish sublinear convergence to a stationary point of the maximum likelihood problem. Numerical results on both synthetic and real data 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 and Venkataraman, Ashwin and Zhao, Xinyi, Estimating Large-Scale Tree Logit Models (November 20, 2022). 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 California 90089
United States

Ashwin Venkataraman

Jindal School of Management, UT Dallas ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

Xinyi Zhao

New York University (NYU) - Leonard N. Stern School of Business ( email )

44 West 4th Street
Suite 9-160
New York, NY NY 10012
United States

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