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Learning Structure in Nested Logit Models

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

Abstract

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.

Citation extraction

46
references
59
in-text mentions
46
distinct cited
3
self-citations
12,177
main-text words

appendix boundary found by appendix_titled_section at “A. Appendix” · 85% of the source is main text. Read the extracted text to check this.

Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Ben-Akiva, M. E. and S. R. Lerman (1985) Discrete choice analysis: theory and application to travel demand, Volume 9 self0.73732100%
2Daly, A (1987) Estimating “tree” logit models0.69351100%
3Fletcher, R. and S. Leyffer (1994) Solving mixed integer nonlinear programs by outer approximation0.64422100%
4Hensher, D. A. and W. H. Greene (2002) Specification and estimation of the nested logit model: alternative normalisations0.64422100%
5Pearce, R. H (2019) Towards a general formulation of lazy constraints0.64422100%
6Benson, A. R., R. Kumar, and A. Tomkins (2016) On the relevance of irrelevant alternatives0.51121100%
7Greene, W. H (2003) Econometric analysis0.51121100%
8McFadden, D (1978) Modeling the choice of residential location0.51121100%
9McFadden, D. and K. Train (1978) An application of diagnostic tests for the independence from irrelevant alternatives property of the multinomial logit model0.51121100%
10Dunning, I., J. Huchette, and M. Lubin (2017) Jump: A modeling language for mathematical optimization0.40511100%

Showing the top 10 of 46 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Discrete Choice Analysis with Machine Learning Capabilities0.73732
2Sparse Covariance Estimation in Logit Mixture Models0.40511