Journal of Statistical Theory and Practice

, Volume 8, Issue 2, pp 367–381 | Cite as

Optimal Designs for Stated Choice Experiments Generated From Fractional Factorial Designs

  • Stephen BushEmail author


This article gives optimal designs obtained by developing a fractional factorial design for the estimation of main effects in stated choice experiments under the assumption of equal selection probabilities. This construction approach follows that of Burgess and Street (2005), who develop complete factorial designs to construct optimal designs for choice experiments, but we obtain choice experiments with fewer choice sets. We construct the fractional factorial designs using the Rao-Hamming method, which assumes all attributes have the same number of levels, which must be a prime or a prime power. We also find optimal designs for stated choice experiments that are generated from asymmetric fractional factorial designs constructed using expansive replacement under the same assumption. We use the multinomial logit model to analyze the results, and we make the assumption of equal selection probabilities when calculating optimality properties. The methods that we use to implement these constructions are given in the last section.


Multiple comparisons Bradley-Terry model Multinomial logit model Rao-Hamming construction Expansive replacement 

AMS Subject Classification

62K05 05B15 


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  1. Bradley, R. A., and M. E. Terry. 1952. Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika, 39, 324–345.MathSciNetzbMATHGoogle Scholar
  2. Burgess, L., and D. J. Street. 2003. Optimal designs for 2k choice experiments. Commun. Stat. Theory Methods, 32, 2185–2206.CrossRefGoogle Scholar
  3. Burgess, L., and D. J. Street. 2005. Optimal designs for choice experiments with asymmetric attributes. J. Stat. Plan. Inference, 134, 288–301.MathSciNetCrossRefGoogle Scholar
  4. Burgess, L., D. J. Street, and N. Wasi. 2011. Comparing designs for choice experiments: A case study. J. Stat. Theory Pract., 5, 25–46.MathSciNetCrossRefGoogle Scholar
  5. Carson, R. T., J. J. Louviere, and E. Wei. 2009. Alternative Australian climate change plans: The public’s views. Energy Policy, 38, 902–911.CrossRefGoogle Scholar
  6. El-Helbawy, A. T., and R. A. Bradley. 1978. Treatment contrasts in paired comparisons: Large-sample results, applications, and some optimal designs. J. Am. Stat. Assoc., 73, 831–839.MathSciNetCrossRefGoogle Scholar
  7. Graßhoff, U., H. Großmann, H. Holling, and R. Schwabe. 2004. Optimal designs for main effects in linear paired comparison models. J. Stat. Plan. Inference, 126, 361–376.MathSciNetCrossRefGoogle Scholar
  8. Graßhoff, U., and R. Schwabe. 2008. Optimal design for the Bradley-Terry paired comparison model. Stat. Methods Appl., 17, 275–289.MathSciNetCrossRefGoogle Scholar
  9. Großmann, H., H. Holling, U. Graßhoff, and R. Schwabe. 2007. A comparison of efficient designs for choices between two options. In MODA 8—Advances in model-oriented design and analysis, 83–90. Heidelberg, Germany: Physica-Verlag.CrossRefGoogle Scholar
  10. Hamming, R. W. 1950. Error-detecting and error correcting codes. Bell System Tech. J., 29, 147–160.MathSciNetCrossRefGoogle Scholar
  11. Hedayat, A. S., N. J. A. Sloane, and J. Stufken. 1999. Orthogonal arrays: Theory and applications. New York, NY: Springer-Verlag.CrossRefGoogle Scholar
  12. Jaeger, S. R., and J. M. Rose. 2008. Stated choice experimentation, contextual influences and food choice: A case study. Food Quality Pref., 19, 539–564.CrossRefGoogle Scholar
  13. Kessels, R., B. Jones, P. Goos, and M. Vandebroek. 2009. An efficient algorithm for constructing Bayesian optimal choice designs. J. Business Econ. Stat., 27, 279–291.MathSciNetCrossRefGoogle Scholar
  14. Lancsar, E. J., J. P. Hall, M. King, P. Kenny, J. J. Louviere, D. G. Fiebig, I. Hossain, F. C. K. Thien, H. K. Reddel, and C. R. Jenkins. 2007. Using discrete choice experiments to investigate subject preferences for preventive asthma medication. Respirology, 12, 127–136.CrossRefGoogle Scholar
  15. Louviere, J. J., D. A. Hensher, and J. D. Swait. 2000. Stated choice methods. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
  16. Rao, C. R. 1947. Factorial experiments derivable from combinatorial arrangements of arrays. Suppl. J. R. Stat. Soc., 9, 128–139.MathSciNetCrossRefGoogle Scholar
  17. Rao, C. R. 1949. On a class of arrangements. Proc. Edinbourough Math. Soc., 8, 119–125.MathSciNetCrossRefGoogle Scholar
  18. Street, D. J., and L. Burgess. 2004. Optimal and near-optimal pairs for the estimation of effects in 2-level choice experiments. J. Stat. Plan. Inference, 118, 185–199.MathSciNetCrossRefGoogle Scholar
  19. Street, D. J., and L. Burgess. 2007. The construction of optimal stated choice experiments: Theory and methods. Hoboken NJ: Wiley.CrossRefGoogle Scholar
  20. Street, D. J., L. Burgess, and J. J. Louviere. 2005. Quick and easy choice sets: Constructing optimal and nearly optimal stated choice experiments. Int. J. Res. Marketing, 22, 459–470.CrossRefGoogle Scholar
  21. Street, D. J., and L. Burgess. 2008. Some open combinatorial problems in the design of stated choice experiments. Discrete Math., 308, 2781–2788.MathSciNetCrossRefGoogle Scholar
  22. Train, K. E. 2003. Discrete choice methods with simulation. New York, NY: Cambridge University Press.CrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2014

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity of Technology SydneySydneyAustralia

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