QME

, 7:69 | Cite as

Studying the level-effect in conjoint analysis: An application of efficient experimental designs for hyper-parameter estimation

  • Qing Liu
  • Angela Dean
  • David Bakken
  • Greg M. Allenby
Article

Abstract

Research in marketing, and business in general, involves understanding when effect-sizes are expected to be large and when they are expected to be small. An example is the understanding of the level-effect in marketing, where the effect of product attributes on utility is positively related to the number of levels present among choice alternatives. Knowing when consumers are sensitive to the competing levels of attributes is an important aspect of merchandising, selling and promotion. In this paper, we propose a model and a method for studying the level-effect in conjoint analysis. The model combines perceptual theories in psychology to arrive at a non-linear specification of hyper-parameters in a hierarchical model. The method applies an experimental design criterion for efficient estimation of hyper-parameters. The proposed model and method are validated using a national sample of respondents.

Keywords

Hierarchical Bayes Conjoint Level effect 

JEL Classification

C11 C31 M31 

Notes

Acknowledgements

We would like to thank the two anonymous referees and the editor Peter Rossi for helpful comments which led to a much improved paper.

References

  1. Atkinson, A. C., & Donev, A. N. (1992). Optimum experimental designs. Oxford: Clarendon Press.Google Scholar
  2. Berger, J. O. (1985). Statistical decision theory and Bayesian analysis. New York: Springer.Google Scholar
  3. Chaloner, K., & Verdinelli, I. (1995). Bayesian experimental design: A review. Statistical Science, 10(3), 273–304. doi: 10.1214/ss/1177009939.CrossRefGoogle Scholar
  4. Cooke, A. D. J., Janiszewski, C., Cunha Jr., M., Nasco, S. A., & De Wilde, E. (2004). Stimulus context and the formation of consumer ideals. The Journal of Consumer Research, 31, 112–124 (June). doi: 10.1086/383428.CrossRefGoogle Scholar
  5. Creyer, E., & Ross, W. T. (1988). The effects of range-frequency manipulations on conjoint importance weight stability. Advances in Consumer Research. Association for Consumer Research (U. S.), 15, 505–509.Google Scholar
  6. Currim, I. S., Weinberg, C. B., & Wittink, D. R. (1981). Design of subscription programs for a performing arts series. The Journal of Consumer Research, 8, 67–75 (June). doi: 10.1086/208842.CrossRefGoogle Scholar
  7. Gamerman, D. (1997). Markov chain Monte Carlo. London: Chapman & Hall.Google Scholar
  8. Han, C., & Chaloner, K. (2004). Bayesian experimental design for nonlinear mixed-effects models with applications to HIV dynamics. Biometrics, 60, 25–33. doi: 10.1111/j.0006-341X.2004.00148.x.CrossRefGoogle Scholar
  9. Huber, J., Payne, J. W., & Puto, C. (1982). Adding asymmetrically dominated alternatives: Violations of regularity and the similarity hypothesis. The Journal of Consumer Research, 9, 90–98 (June). doi: 10.1086/208899.CrossRefGoogle Scholar
  10. Krumhansl, C. L. (1978). Concerning the applicability of geometric models to similarity data: The interrelationship between similarity and spatial density. Psychological Review, 85(5), 445–463. doi: 10.1037/0033-295X.85.5.445.CrossRefGoogle Scholar
  11. Kuhfeld, W. F. (2005). Experimental design, efficiency, coding and choice designs, Tech. rep., SAS TS-722C, http://support.sas.com/techsup/tnote/tnote_stat.html.
  12. Lenk, P. J., Desarbo, W. S., Green, P. E., & Young, M. R. (1996). Hierarchical Bayes conjoint analysis: Recovery of Partworth heterogeneity from reduced experimental designs. Marketing Science, 15(2), 173–191.CrossRefGoogle Scholar
  13. Liu, Q., Dean, A. M., & Allenby, G. M. (2007), Design optimality for hyper-parameter estimation in hierarchical linear models, http://research3.bus.wisc.edu/qliu, Working paper.
  14. Lynch, J. G., Chakravarti, D., & Mitra, A. (1991). Contrast effects in consumer judgments: Changes in mental representations or in the anchoring of rating scales? The Journal of Consumer Research, 18, 284–297 (December). doi: 10.1086/209260.CrossRefGoogle Scholar
  15. Mentre, F., Mallet, A., & Baccar, D. (1997). Optimal design in random-effects regression models. Biometrika, 84(2), 429–442. doi: 10.1093/biomet/84.2.429.CrossRefGoogle Scholar
  16. Parducci, A. (1965). Category judgment: A range-frequency model. Psychological Review, 72, 407–418. doi: 10.1037/h0022602.CrossRefGoogle Scholar
  17. Parducci, A. (1974). Contextual effects: A range-frequency analysis. In E. Carterette, & M. Friedman (Eds.), Handbook of perception (pp. 127–141). New York: Academic Press.Google Scholar
  18. Parducci, A. (1982). Category ratings: still more contextual effects. In B. Wegener (Ed.), Social attitudes and psychophysical measurement (pp. 89–105). Hillsdale: Erlbaum.Google Scholar
  19. Parducci, A., & Wedell, D. H. (1986). The category effect with rating scales: number of categories, number of stimuli, and method of presentation. Journal of Experimental Psychology: Human Perception and Performance, 12, 496–516.CrossRefGoogle Scholar
  20. Rossi, P. E., Allenby, G. M., & McCulloch, R. (2005). Bayesian statistics and marketing. New York: Wiley.Google Scholar
  21. Sandor, Z., & Wedel, M. (2002). Profile construction in experimental choice designs for mixed logit models. Marketing Science, 21(4), 455–475. doi: 10.1287/mksc.21.4.455.131.CrossRefGoogle Scholar
  22. Scheffé, H. (1959). Analysis of variance. New York: Wiley.Google Scholar
  23. Simonson, I., & Tversky, A. (1992). Choice in context: tradeoff contrast and extremeness aversion. JMR, Journal of Marketing Research, 29(3), 281–295. doi: 10.2307/3172740.CrossRefGoogle Scholar
  24. Steenkamp, J.-B. E. M., & Wittink, D. R. (1994). The metric quality of full-profile judgments and the number-of-attribute-levels effect in conjoint analysis. International Journal of Research in Marketing, 11, 275–286. doi: 10.1016/0167-8116(94)90006-X.CrossRefGoogle Scholar
  25. Tod, M., Mentre, F., Merle, Y., & Mallet, A. (1998). Robust optimal design for the estimation of hyper-parameters in population pharmacokinetics. Journal of Pharmacokinetics and Biopharmaceutics, 26, 689–716. doi: 10.1023/A:1020703007613.CrossRefGoogle Scholar
  26. Verlegh, P. W. J., Schifferstein, H. N. J., & Wittink, D. R. (2002). Range and number-of-levels effects in derived and stated measures of attribute importance. Marketing Letters, 13(1), 41–52.CrossRefGoogle Scholar
  27. Wedell, D. H., Parducci, A., & Roman, D. (1989). Student perceptions of fair grading: a range-frequency analysis. The American Journal of Psychology, 102, 233–248.CrossRefGoogle Scholar
  28. Wittink, D. R., Huber, J., Zandan, P., & Johnson, R. M. (1992). The number of levels effect in conjoint: where does it come from, and can it be eliminated? in Sawtooth Software Conference Proceedings.Google Scholar
  29. Wittink, D. R., Krishnamurthi, L., & Nutter, J. B. (1982). Comparing derived importance weights across attributes. The Journal of Consumer Research, 8, 471–474. doi: 10.1086/208890.CrossRefGoogle Scholar
  30. Wittink, D. R., Krishnamurthi, L., & Reibstein, D. J. (1990). The effect of differences in the number of attribute levels on conjoint analysis. Marketing Letters, 1(2), 113–123. doi: 10.1007/BF00435295.CrossRefGoogle Scholar
  31. Wittink, D. R., McLauchlan, W. G., & Seetharaman, P. B. (1997). Solving the number-of-attribute-levels problem in conjoint analysis. in Sawtooth Software Conference proceedingsGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Qing Liu
    • 1
  • Angela Dean
    • 2
  • David Bakken
    • 3
  • Greg M. Allenby
    • 4
  1. 1.Department of MarketingUniversity of Wisconsin-MadisonMadisonUSA
  2. 2.Department of StatisticsOhio State UniversityColumbusUSA
  3. 3.Harris InteractiveRochesterUSA
  4. 4.Fisher College of BusinessOhio State UniversityColumbusUSA

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