Abstract
Sun and Dean proposed an approach for finding A-optimal and A-efficient discrete choice designs without a large computational effort, for estimating orthonormal contrasts, and for both balanced and unbalanced profile utilities. Their method was based on the “contribution” made by each choice set to the contrasts being estimated, and was illustrated for the setting of two-level attributes and orthonormal main effect and interaction contrasts. In this article, the use of the Sun and Dean methodology is extended to encompass pairwise comparisons. The methodology is illustrated for the construction of A-efficient designs for attributes having different numbers of levels and where contrasts of interest are either orthonormal factorial contrasts or pairwise comparisons in the attribute levels. When the designs are large, issues involved with finding smaller subdesigns are discussed briefly.
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Burgess, L., and D. J. Street. 2005. Optimal designs for choice experiments with asymmetric attributes. Journal of Statistical Planning and Inference 134 (1):288–301.
Bush, S., L. Burgess, and D. Street. 2010. Optimal designs for stated choice experiments that incorporate ties. Journal of Statistical Planning and Inference 140 (7):1712–1718.
Crabbe, M., B. Jones, and M. Vandebroek. 2013. Comparing two-stage segmentation methods for choice data with a one-stage latent class choice analysis. Communications in Statistics-Simulation and Computation 42 (5):1188–1212.
Goos, P., B. Vermeulen, and M. Vandebroek. 2010. D-optimal conjoint choice designs with no-choice options for a nested logit model. Journal of Statistical Planning and Inference 140 (4):851–861.
Graßhoff, U., and R. Schwabe. 2008. Optimal design for the Bradley–Terry paired comparison model. Statistical Methods and Applications 17 (3):275–289.
Großmann, H., and R. Schwabe. 2015. Design for discrete choice experiments. In Handbook of design and analysis of experiments, ed. A. M. Dean, M. D. Morris, J. Stufken, and D. Bingham, 787–832. Boca Raton, FL: Chapman and Hall/CRC.
Huber, J., and K. Zwerina. 1996. The importance of utility balance in efficient choice designs. Journal of Marketing Research 33 (3):307–317.
Lancsar, E., J. Louviere, C. Donaldson, G. Currie, and L. Burgess. 2013. Best worst discrete choice experiments in health: Methods and an application. Social Science & Medicine 76:74–82.
Liu, Q., A. M. Dean, D. Bakken, and G. Allenby. 2009. Efficient experimental designs for hyperparameter estimation: Studying the level effect in conjoint analysis. Quantitative Marketing and Economics 7:69–93.
Ruan, S., S. MacEachern, T. Otter, and A. Dean. 2008. The dependent poisson race model and modeling dependence in conjoint choice experiments. Psychometrika 73 (2):261–88.
Singh, R., F.-S. Chai, and A. Das. 2015. Optimal two-level choice designs for any number of choice sets. Biometrika 102 (4):967–973.
Street, D., and L. Burgess. 2007. The construction of optimal stated choice experiments: Theory and methods. Hoboken, NJ: John Wiley & Sons.
Street, D. J., L. Burgess, and J. J. Louviere. 2005. Quick and easy choice sets: Constructing optimal and nearly optimal stated choice experiments. International Journal of Research in Marketing 22 (4):459–70.
Sun, F. 2012. On A-optimal designs for discrete choice experiments and sensitivity analysis for computer experiments. PhD thesis, Ohio State University, Columbus, OH.
Sun, F., and A. Dean. 2016. A-optimal and A-efficient designs for discrete choice experiments. Journal of Statistical Planning and Inference 170:144–57.
Train, K. E. 2009. Discrete choice methods with simulation, 2nd ed. Cambridge, UK: Cambridge University Press.
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Sun, F., Dean, A. A-efficient discrete choice designs for attributes with unequal numbers of levels. J Stat Theory Pract 11, 322–338 (2017). https://doi.org/10.1080/15598608.2017.1292482
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DOI: https://doi.org/10.1080/15598608.2017.1292482