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Minimum aberration designs for discrete choice experiments. (English) Zbl 1427.62086

Summary: A discrete choice experiment (DCE) is a survey method that gives insight into individual preferences for particular attributes. Traditionally, methods for constructing DCEs focus on identifying the individual effect of each attribute (a main effect). However, an interaction effect between two attributes (a two-factor interaction) better represents real-life trade-offs, and provides us a better understanding of subjects’ competing preferences. In practice it is often unknown which two-factor interactions are significant. To address the uncertainty, we propose the use of minimum aberration blocked designs to construct DCEs. Such designs maximize the number of models with estimable two-factor interactions in a DCE with two-level attributes. We further extend the minimum aberration criteria to DCEs with mixed-level attributes and develop some general theoretical results.

MSC:

62K15 Factorial statistical designs
62J15 Paired and multiple comparisons; multiple testing
62K10 Statistical block designs

Software:

DoE.base
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References:

[1] Atkinson, A., and A. Donev. 1992. Optimum experimental designs. Oxford, UK: Oxford University Press. · Zbl 0829.62070
[2] Bliemer, M.; Rose, J., Experimental design influences on stated choice output: An empirical study in air travel choice, Transportation Research Part A: Policy and Practice, 45, 63-79 (2011)
[3] Bunch, D. S., J. J. Louviere, and D. Anderson. 1996. A comparison of experimental design strategies for choice-based conjoint analysis with generic-attribute multinomial logit models. Working paper, Graduate School of Management, University of California, Davis, California.
[4] Burgess, L.; Street, D. J.; Wasi, N., Comparing designs for choice experiments: a case study, Journal of Statistical Theory and Practice, 5, 25-46 (2011) · Zbl 05902633 · doi:10.1080/15598608.2011.10412048
[5] Burgess, L.; Knox, S. A.; Street, D. J.; Norman, R., Comparing designs constructed with and without priors for choice experiments: A case study, Journal of Statistical Theory and Practice, 9, 330-60 (2015) · Zbl 1425.62092 · doi:10.1080/15598608.2014.905223
[6] Bush, S., Optimal designs for stated choice experiments generated from fractional factorial designs, Journal of Statistical Theory and Practice, 8, 367-81 (2014) · Zbl 1423.62075 · doi:10.1080/15598608.2013.805451
[7] Butler, N. A., Minimum G2-aberration properties of two-level foldover designs, Statistics Probability Letters, 67, 121-32 (2004) · Zbl 1059.62082 · doi:10.1016/j.spl.2003.09.011
[8] Chen, H.; Cheng, C. S., Theory of optimal blocking of 2n-m designs, Annals of Statistics, 27, 1948-73 (1999) · Zbl 0961.62066 · doi:10.1214/aos/1017939246
[9] Cheng, C. S. 2014. Theory of factorial design: Single- and multi-stratum experiments. Boca Raton, FL: Chapman and Hall/CRC. · Zbl 1306.62007
[10] Cheng, C. S.; Mee, R. W.; Yee, O., Second order saturated orthogonal arrays of strength three, Statistica Sinica, 18, 105-19 (2008) · Zbl 1137.62049
[11] Cheng, C. S.; Mukerjee, R., Blocked regular fractional factorial designs with maximum estimation capacity, Annals of Statistics, 29, 530-48 (2001) · Zbl 1041.62064 · doi:10.1214/aos/1009210551
[12] Cheng, C. S.; Steinberg, D. M.; Sun, D. X., Minimum aberration and model robustness for two-level factorial designs, Journal of the Royal Statistical Society: Series, B 61, 85-93 (1999) · Zbl 0913.62072 · doi:10.1111/1467-9868.00164
[13] Cheng, S. W.; Li, W.; Ye, K. Q., Blocked nonregular two-level factorial designs, Technometrics, 46, 269-79 (2004) · doi:10.1198/004017004000000301
[14] Dey, A., and R. Mukerjee. 1999. Fractional factorial plans. New York, NY: Wiley. · Zbl 0930.62081 · doi:10.1002/9780470316986
[15] Fries, A.; Hunter, W. G., Minimum aberration 2k-p designs, Technometics, 22, 601-8 (1980) · Zbl 0453.62063
[16] Gerard, Karen; Shanahan, Marian; Louviere, Jordan, Using Discrete Choice Modelling to Investigate Breast Screening Participation, 117-137 (2008), Dordrecht
[17] Groemping, U., B. Amarov, and H. Xu. 2015. DoE.base: R package version 0.27-1. https://doi.org/CRAN.R-project.org/package=DoE.base. August 21.
[18] Groemping, U.; Xu, H., Generalized resolution for orthogonal arrays, Annals of Statistics, 42, 918-39 (2014) · Zbl 1305.62291 · doi:10.1214/14-AOS1205
[19] Grossmann, H.; Schwabe, R.; Dean, A. (ed.); Morris, M. (ed.); Stufken, J. (ed.); Bingham, D. (ed.), Design for discrete choice experiments, 787-826 (2015), Boca Raton, FL · Zbl 1383.62196
[20] Hedayat, A. S., N. J. A. Sloane, and J. Stufken. 1999. Orthogonal arrays: Theory and applications. New York, NY: Springer-Verlag. · Zbl 0935.05001 · doi:10.1007/978-1-4612-1478-6
[21] Jaynes, J.; Wong, W. K.; Xu, H., Using blocked fractional factorial designs to construct discrete choice experiments for healthcare studies, Statistics in Medicine, 35, 2543-60 (2016) · doi:10.1002/sim.6882
[22] Johnson, F. R.; Lancsar, E.; Marshall, D.; Kilambi, V.; Muhlbacher, A.; Regier, D. A.; Bresnahan, B. W.; Kanninen, B.; Bridges, J. F P., Constructing experimental designs for discrete-choice experiments: Report of the ISPOR Conjoint Analysis Experimental Design Good Research Practices Task Force, Value in Health, 16, 3-13 (2013) · doi:10.1016/j.jval.2012.08.2223
[23] Kessels, R.; Jones, B.; Goos, P.; Vandebroek, M., The usefulness of Bayesian optimal designs for discrete choice experiments, Applied Stochastic Models in Business and Industry, 27, 173-88 (2011) · doi:10.1002/asmb.906
[24] Kuhfeld, W.; Tobias, R., Large factorial designs for product engineering and market research applications, Technometrics, 47, 122-32 (2005) · doi:10.1198/004017004000000653
[25] Lancsar, E.; Louviere, J., Conducting discrete choice experiments to inform healthcare decision making, Pharmacoeconomics, 26, 661-77 (2008) · doi:10.2165/00019053-200826080-00004
[26] Li, W.; Nachtsheim, C. J.; Wang, K.; Reul, R.; Albrecht, M., Conjoint analysis and discrete choice experiments for quality improvement, Journal of Quality Technology, 45, 74-99 (2013) · doi:10.1080/00224065.2013.11917916
[27] Mukerjee, R., and C. F. J. Wu. 2006. A modern theory of factorial designs. New York, NY: Springer. · Zbl 1271.62179
[28] Sandor, Z.; Wedel, M., Conjoint choice experiments using managers’ prior beliefs, Journal of Marketing Research, 38, 430-44 (2001) · doi:10.1509/jmkr.38.4.430.18904
[29] Sitter, R. R.; Chen, J.; Feder, M., Fractional resolution and minimum aberration in blocked 2n-k designs, Technometrics, 39, 382-90 (1997) · Zbl 0913.62073
[30] Street, D., and L. Burgess. 2007. The construction of optimal stated choice experiments: Theory and methods. New York, NY: Wiley. · Zbl 1258.62008 · doi:10.1002/9780470148563
[31] Sun, D. X.; Wu, C. F J.; Chen, Y., Optimal blocking schemes for 2n and 2n-p designs, Technometrics, 39, 298-307 (1997) · Zbl 0891.62055
[32] Viney, R.; Savage, E.; Louviere, J., Empirical investigation of experimental design properties of discrete choice experiments in health care, Health Economics, 14, 349-362 (2005) · doi:10.1002/hec.981
[33] Wu, C. F. J., and M. Hamada. 2009. Experiments: Planning, analysis and optimization, 2nd ed. New York, NY: Wiley. · Zbl 1229.62100
[34] Xu, H., Minimum moment aberration for nonregular designs and supersaturated designs, Statistica Sinica, 13, 691-708 (2003) · Zbl 1028.62063
[35] Xu, H., Blocked regular fractional factorial designs with minimum aberration, Annals of Statistics, 34, 2534-53 (2006) · Zbl 1106.62087 · doi:10.1214/009053606000000777
[36] Xu, H.; Dean, A. (ed.); Morris, M. (ed.); Stufken, J. (ed.); Bingham, D. (ed.), Nonregular factorial and supersaturated designs, 339-70 (2015), Boca Raton, FL · Zbl 1369.62188
[37] Xu, H.; Lau, S., Minimum aberration blocking schemes for two- and three-level FFDs, Journal of Statistical Planning and Inference, 136, 4088-118 (2006) · Zbl 1104.62090 · doi:10.1016/j.jspi.2005.05.002
[38] Xu, H.; Mee, R. W., Minimum aberration blocking schemes for 128-run designs, Journal of Statistical Planning and Inference, 140, 3213-29 (2010) · Zbl 1204.62134 · doi:10.1016/j.jspi.2010.04.009
[39] Xu, H.; Phoa, F. K H.; Wong, W. K., Recent developments in nonregular fractional factorial designs, Statistics Surveys, 3, 18-46 (2009) · Zbl 1300.62056 · doi:10.1214/08-SS040
[40] Zhang, R.; Park, D., Optimal blocking of two-level fractional factorial designs, Journal of Statistical Planning and Inference, 91, 107-21 (2000) · Zbl 0958.62072 · doi:10.1016/S0378-3758(00)00133-6
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