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Nonparametric Estimation of Choice Models

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The Elements of Joint Learning and Optimization in Operations Management

Part of the book series: Springer Series in Supply Chain Management ((SSSCM,volume 18))

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Abstract

Choice-based demand models serve as building blocks for making demand predictions, which are key inputs to critical operational decisions, such as what prices to charge for different products or which subset of products to offer to the customers. Traditionally, parametric choice models (such as the multinomial logit model) have been employed for tractability reasons, but with the increasing ability of firms to collect large volumes of sales transaction and product availability data, nonparametric choice models have been gaining in popularity. We review recent advances in nonparametric estimation of two versatile choice model families.

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Notes

  1. 1.

    However, they did not introduce this nomenclature.

  2. 2.

    There are numerous papers that explicitly account for the demand censoring issue while estimating the choice model; see, for instance, Haensel and Koole (2011), Newman et al. (2014), and Abdallah and Vulcano (2020).

  3. 3.

    This is true as long as \(\left <\nabla h (\boldsymbol {x}^{(k-1)}), \boldsymbol {v}^{(k)} - \boldsymbol {x}^{(k-1)}\right > < 0\). If \(\left <\nabla h (\boldsymbol {x}^{(k-1)}), \boldsymbol {v}^{(k)} - \boldsymbol {x}^{(k-1)}\right > \geq 0\), then the convexity of h(⋅) implies that h(x) ≥ h(x(k−1)) for all \(\boldsymbol {x} \in \mathcal {D}\) and consequently, x(k−1) is an optimal solution.

  4. 4.

    We abuse notation and denote αf(σ) as ασ for any \(\sigma \in \mathcal {P}\) in the remainder of this section.

  5. 5.

    Mišić (2016) also proposed a similar formulation for estimating the rank-based choice model with an L1-norm loss function using a column generation approach.

  6. 6.

    The remaining products in each ranking can be chosen arbitrarily.

  7. 7.

    In this case, the feature vector for other products would typically include a constant feature 1 to allow for general no-purchase market shares.

  8. 8.

    Our development here is closely related to that in JSV but with slight differences.

  9. 9.

    Technically, the distribution is modeled over the parameter vector β as opposed to its “type” representation f(β).

  10. 10.

    This is equivalent to minimizing the KL-divergence loss function and is the standard choice when estimating the mixed logit model.

  11. 11.

    The rank-based model can allow for the number of products in a ranking to be strictly smaller than the size of the product universe, in which case the customer selects the no-purchase option if none of the products in the ranking is part of the offer set.

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Authors and Affiliations

  1. Stern School of Business, New York University, New York, NY, USA

    Srikanth Jagabathula

  2. Jindal School of Management, University of Texas at Dallas, Richardson, TX, USA

    Ashwin Venkataraman

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  1. Srikanth Jagabathula
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  2. Ashwin Venkataraman
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Correspondence to Ashwin Venkataraman .

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Editors and Affiliations

  1. New York University, New York, NY, USA

    Xi Chen

  2. University of Michigan–Ann Arbor, Ann Arbor, MI, USA

    Stefanus Jasin

  3. University of Michigan–Ann Arbor, Ann Arbor, MI, USA

    Cong Shi

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Jagabathula, S., Venkataraman, A. (2022). Nonparametric Estimation of Choice Models. In: Chen, X., Jasin, S., Shi, C. (eds) The Elements of Joint Learning and Optimization in Operations Management. Springer Series in Supply Chain Management, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-031-01926-5_8

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