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Bayesian D-Optimal Choice Designs for Mixtures

Author

Listed:
  • Aiste Ruseckaite

    (Erasmus University Rotterdam)

  • Peter Goos

    (Universiteit Antwerpen, Belgium)

  • Dennis Fok

    (Erasmus University Rotterdam)

Abstract

Consumer products and services can often be described as mixtures of ingredients. Examples are the mixture of ingredients in a cocktail and the mixture of different components of waiting time (e.g., in-vehicle and out-of-vehicle travel time) in a transportation setting. Choice experiments may help to determine how the respondents' choice of a product or service is affected by the combination of ingredients. In such studies, individuals are confronted with sets of hypothetical products or services and they are asked to choose the most preferred product or service from each set. However, there are no studies on the optimal design of choice experiments involving mixtures. We propose a method for generating an optimal design for such choice experiments. To this end, we first introduce mixture models in the choice context and next present an algorithm to construct optimal experimental designs, assuming the multinomial logit model is used to analyze the choice data. To overcome the problem that the optimal designs depend on the unknown parameter values, we adopt a Bayesian D-optimal design approach. We also consider locally D-optimal designs and compare the performance of the resulting designs to those produced by a utility-neutral (UN) approach in which designs are based on the assumption that individuals are indifferent between all choice alternatives. We demonstrate that our designs are quite different and in general perform better than the UN designs.

Suggested Citation

  • Aiste Ruseckaite & Peter Goos & Dennis Fok, 2014. "Bayesian D-Optimal Choice Designs for Mixtures," Tinbergen Institute Discussion Papers 14-057/III, Tinbergen Institute.
  • Handle: RePEc:tin:wpaper:20140057
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    References listed on IDEAS

    as
    1. Bliemer, Michiel C.J. & Rose, John M., 2010. "Construction of experimental designs for mixed logit models allowing for correlation across choice observations," Transportation Research Part B: Methodological, Elsevier, vol. 44(6), pages 720-734, July.
    2. Heiko Großmann & Heinz Holling & Ulrike Graßhoff & Rainer Schwabe, 2006. "Optimal Designs for Asymmetric Linear Paired Comparisons with a Profile Strength Constraint," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 64(1), pages 109-119, August.
    3. Bliemer, Michiel C.J. & Rose, John M. & Hensher, David A., 2009. "Efficient stated choice experiments for estimating nested logit models," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 19-35, January.
    4. Jie Yu & Peter Goos & Martina Vandebroek, 2009. "Efficient Conjoint Choice Designs in the Presence of Respondent Heterogeneity," Marketing Science, INFORMS, vol. 28(1), pages 122-135, 01-02.
    5. 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.
    6. Train,Kenneth E., 2009. "Discrete Choice Methods with Simulation," Cambridge Books, Cambridge University Press, number 9780521747387.
    7. Bart Vermeulen & Peter Goos & Riccardo Scarpa & Martina Vandebroek, 2011. "Bayesian Conjoint Choice Designs for Measuring Willingness to Pay," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 48(1), pages 129-149, January.
    8. John M. Rose & Michiel C. J. Bliemer, 2008. "Constructing Efficient Stated Choice Experimental Designs," Transport Reviews, Taylor & Francis Journals, vol. 29(5), pages 587-617, October.
    9. Yu, Jie & Goos, Peter & Vandebroek, Martina, 2010. "Comparing different sampling schemes for approximating the integrals involved in the efficient design of stated choice experiments," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1268-1289, December.
    10. Hensher, David A. & Rose, John M., 2009. "Simplifying choice through attribute preservation or non-attendance: Implications for willingness to pay," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 45(4), pages 583-590, July.
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    Cited by:

    1. Zijlstra, Toon & Goos, Peter & Verhetsel, Ann, 2019. "A mixture-amount stated preference study on the mobility budget," Transportation Research Part A: Policy and Practice, Elsevier, vol. 126(C), pages 230-246.

    More about this item

    Keywords

    Bayesian design; Choice experiments; D-optimality; Experimental design; Mixture coordinate-exchange algorithm; Mixture experiment; Multinomial logit model; Optimal design;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C83 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Survey Methods; Sampling Methods
    • C90 - Mathematical and Quantitative Methods - - Design of Experiments - - - General
    • C99 - Mathematical and Quantitative Methods - - Design of Experiments - - - Other

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