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A-optimal designs under a linearized model for discrete choice experiments

Author

Listed:
  • Rakhi Singh

    (University of North Carolina at Greensboro)

  • Angela Dean

    (The Ohio State University)

  • Ashish Das

    (Indian Institute of Technology Bombay)

  • Fangfang Sun

    (Harbin Institute of Technology)

Abstract

Discrete choice experiments have proven useful in areas such as marketing, government planning, medical studies and psychological research, to help understand consumer preferences. To aid in these experiments, several groups of authors have contributed to the theoretical development of D-optimal and A-optimal discrete choice designs under the multinomial logit (MNL) model. In the setting in which the class of feasible designs is too large for complete search, Sun and Dean (J Stat Plann Inference 170:144–157, 2016) proposed a construction method for A-optimal designs for estimating a set of orthonormal contrasts in the option utilities via a linearization of the MNL model. In this paper, we show that the set of A-optimal designs that result from this linearization may or may not include the optimal design under the MNL model itself. We provide an alternative linearization that leads to an information matrix which coincides with that under the MNL model and, consequently, selects the same set of designs as being A-optimal. We obtain a bound for the average variance of a set of contrasts of interest under the MNL model, and show that the construction method of Sun and Dean (2016) can be used to identify A-optimal and A-efficient designs under the MNL model for both equal and unequal utilities.

Suggested Citation

  • Rakhi Singh & Angela Dean & Ashish Das & Fangfang Sun, 2021. "A-optimal designs under a linearized model for discrete choice experiments," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 445-465, May.
  • Handle: RePEc:spr:metrik:v:84:y:2021:i:4:d:10.1007_s00184-020-00771-5
    DOI: 10.1007/s00184-020-00771-5
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    References listed on IDEAS

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    1. Ulrike Graßhoff & Rainer Schwabe, 2008. "Optimal design for the Bradley–Terry paired comparison model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 275-289, July.
    2. Kessels, Roselinde & Jones, Bradley & Goos, Peter & Vandebroek, Martina, 2009. "An Efficient Algorithm for Constructing Bayesian Optimal Choice Designs," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(2), pages 279-291.
    3. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387, October.
    4. Shiling Ruan & Steven MacEachern & Thomas Otter & Angela Dean, 2008. "The Dependent Poisson Race Model and Modeling Dependence in Conjoint Choice Experiments," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 261-288, June.
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    Cited by:

    1. Abdulrahman S. Alamri & Stelios D. Georgiou & Stella Stylianou, 2023. "Construction of symmetric paired choice experiments: minimising runs and maximising efficiency," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-12, December.

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