Youssef M. Aboutaleb, Moshe Ben-Akiva, Patrick Jaillet
arXiv 18 Aug 2020 · Statistics — Methodology · 4 citations (OpenAlex)
arXiv:2008.08048 · PDF · DOI · OpenAlex · Extracted main text
This paper introduces a new data-driven methodology for nested logit structure discovery. Nested logit models allow the modeling of positive correlations between the error terms of the utility specifications of the different alternatives in a discrete choice scenario through the specification of a nesting structure. Current nested logit model estimation practices require an a priori specification of a nesting structure by the modeler. In this we work we optimize over all possible specifications of the nested logit model that are consistent with rational utility maximization. We formulate the problem of learning an optimal nesting structure from the data as a mixed integer nonlinear programming (MINLP) optimization problem and solve it using a variant of the linear outer approximation algorithm. We exploit the tree structure of the problem and utilize the latest advances in integer optimization to bring practical tractability to the optimization problem we introduce. We demonstrate the ability of our algorithm to correctly recover the true nesting structure from synthetic data in a Monte Carlo experiment. In an empirical illustration using a stated preference survey on modes of transportation in the U.S. state of Massachusetts, we use our algorithm to obtain an optimal nesting tree representing the correlations between the unobserved effects of the different travel mode choices. We provide our implementation as a customizable and open-source code base written in the Julia programming language.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Ben-Akiva, M. E. and S. R. Lerman (1985) Discrete choice analysis: theory and application to travel demand, Volume 9 self | 0.737 | 3 | 2 | 100% |
| 2 | Daly, A (1987) Estimating “tree” logit models | 0.693 | 5 | 1 | 100% |
| 3 | Fletcher, R. and S. Leyffer (1994) Solving mixed integer nonlinear programs by outer approximation | 0.644 | 2 | 2 | 100% |
| 4 | Hensher, D. A. and W. H. Greene (2002) Specification and estimation of the nested logit model: alternative normalisations | 0.644 | 2 | 2 | 100% |
| 5 | Pearce, R. H (2019) Towards a general formulation of lazy constraints | 0.644 | 2 | 2 | 100% |
| 6 | Benson, A. R., R. Kumar, and A. Tomkins (2016) On the relevance of irrelevant alternatives | 0.511 | 2 | 1 | 100% |
| 7 | Greene, W. H (2003) Econometric analysis | 0.511 | 2 | 1 | 100% |
| 8 | McFadden, D (1978) Modeling the choice of residential location | 0.511 | 2 | 1 | 100% |
| 9 | McFadden, D. and K. Train (1978) An application of diagnostic tests for the independence from irrelevant alternatives property of the multinomial logit model | 0.511 | 2 | 1 | 100% |
| 10 | Dunning, I., J. Huchette, and M. Lubin (2017) Jump: A modeling language for mathematical optimization | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 46 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Discrete Choice Analysis with Machine Learning Capabilities | 0.737 | 3 | 2 |
| 2 | Sparse Covariance Estimation in Logit Mixture Models | 0.405 | 1 | 1 |