Abstract
A new method to generate designs for estimating main effects and two-factor interactions of two-level attributes from choice experiments is presented for the situation where the choice sets are pairs and the alternatives are specified by a subset of the attributes. Partial-profile designs are constructed by using Hadamard matrices and factorial and incomplete block designs as building blocks. Their information matrix under the multinomial logit model is derived under the indifference assumption of equal choice probabilities by exploiting the relationship between the multinomial logit model for pairs and the linear paired comparison model. The information matrix depends only on the incomplete block designs but not on the other building blocks. Efficient partial-profile designs with relatively small numbers of choice sets are found by performing computer searches inspired by these results.
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References
Alba, J. W., and A. D. J. Cooke. 2004. When absence begets inference in conjoint analysis. Journal of Marketing Research 41:382–87.
Bradley, R. A., and M. E. Terry. 1952. Rank analysis of incomplete block designs: I. The method of paired comparisons. Biometrika 39:324–45.
Bradlow, E. T., Y. Hu, and T.-H. Ho. 2004. A learning-based model for imputing missing levels in partial conjoint profiles. Journal of Marketing Research 41:369–81.
Burgess, L., and D. J. Street. 2003. Optimal designs for 2k choice experiments. Communications in Statistics—Theory and Methods 32:2185–206.
Burgess, L., and D. J. Street. 2005. Optimal designs for choice experiments with asymmetric attributes. Journal of Statistical Planning and Inference 134:288–301.
Chrzan, K. 2010. Using partial profile choice experiments to handle large numbers of attributes. International Journal of Market Research 52:827–40.
Graßhoff, U., H. Großmann, H. Holling, and R. Schwabe. 2003. Optimal paired comparison designs for first-order interactions. Statistics 37:373–86.
Großmann, H., U. Graßhoff, and R. Schwabe. 2009. Approximate and exact optimal designs for paired comparisons of partial profiles when there are two groups of factors. Journal of Statistical Planning and Inference 139:1171–79.
Großmann, H., U. Graßhoff, and R. Schwabe. 2014. A catalogue of designs for partial profiles in paired comparison experiments with three groups of factors. Statistics 48:1268–81.
Großmann, H., H. Holling, U. Graßhoff, and R. Schwabe. 2006. Optimal designs for asymmetric linear paired comparisons with a profile strength constraint. Metrika 64:109–19.
Großmann, H., H. Holling, and R. Schwabe. 2002. Advances in optimum experimental design for conjoint analysis and discrete choice models. In Econometric models in marketing. Vol. 16 of Advances in Econometrics, ed. P. H. Franses and A. L. Montgomery, 93–117. Amsterdam, The Netherlands: JAI Press.
Grossmann, H., and R. Schwabe. 2015. Design for discrete choice experiments. In Handbook of design and analysis of experiments, ed. A. Dean, M. Morris, J. Stufken, and D. Bingham, 787–831. Boca Raton, FL: Chapman & Hall/CRC.
Großmann, H., R. Schwabe, and S. G. Gilmour. 2012. Designs for first-order interactions in paired comparison experiments with two-level factors. Journal of Statistical Planning and Inference 142:2395–401.
Huber, J., and K. Zwerina. 1996. The importance of utility balance in efficient choice designs. Journal of Marketing Research 33:307–17.
Kessels, R., B. Jones, and P. Goos. 2011. Bayesian optimal designs for discrete choice experiments with partial profiles. Journal of Choice Modelling 4:52–74.
Kessels, R., B. Jones, and P. Goos. 2015. An improved two-stage variance balance approach for constructing partial profile designs for discrete choice experiments. Applied Stochastic Models in Business and Industry 31:626–48.
Louviere, J. J., D. A. Hensher, and J. D. Swait. 2000. Stated choice methods: Analysis and application. Cambridge, UK: Cambridge University Press.
Rose, J. M., and M. C. J. Bliemer. 2014. Stated choice experimental design theory: The who, the what and the why. In Handbook of choice modelling, ed. S. Hess, and A. Daly, 152–77. Cheltenham, UK: Edward Elgar Publishing.
Street, D. J., D. S. Bunch, and B. J. Moore. 2001. Optimal designs for 2k paired comparison experiments. Communications in Statistics—Theory and Methods 30:2149–71.
Street, D. J., and L. Burgess. 2004. Optimal and near-optimal pairs for the estimation of effects in 2-level choice experiments. Journal of Statistical Planning and Inference 118:185–99.
Street, D. J., and L. Burgess. 2007. The construction of optimal stated choice experiments: Theory and methods. Hoboken, NJ: Wiley.
Street, D. J., and L. Burgess. 2012. Designs for choice experiments for the multinomial logit model. In Design and analysis of experiments: Special designs and applications, ed. K. Hinkelmann, 331–78. New York, NY: Wiley.
Train, K. E. 2003. Discrete choice methods with simulation. Cambridge, UK: Cambridge University Press.
Wolfram Research, Inc. 2015. Mathematica 10.1. Champaign, IL: Wolfram Research, Inc.
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Großmann, H. Partial-profile choice designs for estimating main effects and interactions of two-level attributes from paired comparison data. J Stat Theory Pract 11, 236–253 (2017). https://doi.org/10.1080/15598608.2016.1197868
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DOI: https://doi.org/10.1080/15598608.2016.1197868