, Volume 31, Issue 12, pp 1169–1183 | Cite as

A Closer Look at Decision and Analyst Error by Including Nonlinearities in Discrete Choice Models: Implications on Willingness-to-Pay Estimates Derived from Discrete Choice Data in Healthcare

  • Esther W. de Bekker-Grob
  • John M. Rose
  • Michiel C. J. Bliemer
Original Research Article



Most researchers in health economics cite random utility theory (RUT) when analysing discrete choice experiments (DCEs). Under RUT, the error term is associated with the analyst’s inability to properly capture the true choice processes of the respondent as well as the inconsistency or mistakes arising from the respondent themselves. Under such assumptions, it stands to reason that analysts should explore more complex nonlinear indirect utility functions, than currently used in healthcare, to strive for better estimates of preferences in healthcare.


To test whether complex indirect utility functions decrease error variance for models that either implicitly (i.e. the multinomial logit (MNL) model) or explicitly (i.e. entropy multinomial logit (EMNL) model) account for error variance in health(care)-related DCEs; and to determine the impact of complex indirect utility functions on willingness-to-pay (WTP) measures.


Using data from DCEs aimed at healthcare-related decisions, we empirically compared (1) complex and simple indirect utility specifications in terms of goodness of fit, (2) their impact on WTP measures, including confidence intervals (CIs) based on the Delta method, the Krinsky and Robb-procedure, and Bootstrapping, and (3) MNL and EMNL model results.


Complex indirect utility functions had a better model fit than simple specifications (p < 0.05). WTP estimates were quite similar across alternative specifications. The Delta method produced the most narrow CIs. The EMNL model showed that respondents apply simplifying strategies when answering DCE questions.


Complex indirect utility functions reduce error arisen from researchers, which can have important implications for measures in healthcare such as the WTP, whereas EMNL provides insights into the behaviour of respondents when answering DCEs. Understanding how respondents answer DCE questions may allow researchers to construct DCEs that minimise scale differences, so that the decision error made across respondents is more homogeneous and therefore taken out as additional noise in the data. Hence, better estimates of preferences in healthcare can be provided.

Supplementary material

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Supplementary material 1 (DOC 127 kb)
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Supplementary material 2 (DOC 58 kb)
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Supplementary material 3 (DOC 34 kb)
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Supplementary material 4 (DOC 64 kb)


  1. 1.
    Louviere JJ, Lancsar E. Choice experiments in health: the good, the bad, the ugly and toward a brighter future. Health Econ Policy Law. 2009;4(Pt 4):527–46.PubMedCrossRefGoogle Scholar
  2. 2.
    Witt J, Scott A, Osborne RH. Designing choice experiments with many attributes: an application to setting priorities for orthopaedic waiting lists. Health Econ. 2009;18(6):681–96.PubMedCrossRefGoogle Scholar
  3. 3.
    Manski C. The structure of random utility models. Theory Decis. 1977;8:229–54.CrossRefGoogle Scholar
  4. 4.
    McFadden D. Conditional logit analysis of qualitative choice behavior. In: Zarembka P, editor. Frontiers in econometrics. New York: Academic Press; 1974. p. 105–42.Google Scholar
  5. 5.
    Fiebig DG, Knox S, Viney R, Haas M, Street DJ. Preferences for new and existing contraceptive products. Health Econ. 2011;20(Suppl 1):35–52.PubMedCrossRefGoogle Scholar
  6. 6.
    Keane M. The generalized logit model: preliminary ideas on a research program Motorola-CenSoC meeting, Hong Kong; 2006.Google Scholar
  7. 7.
    Kuhn HW, Tucker AW. Nonlinear programming. In: Neyman J, editor. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. Berkeley and Los Angeles: University of California Press; 1950. p. 481–492.Google Scholar
  8. 8.
    Johnson FR, Mohamed AF, Ozdemir S, Marshall DA, Phillips KA. How does cost matter in health-care discrete-choice experiments? Health Econ. 2011;20(3):323–30.PubMedCrossRefGoogle Scholar
  9. 9.
    Kolstad JR. How to make rural jobs more attractive to health workers: findings from a discrete choice experiment in Tanzania. Health Econ. 2011;20(2):196–211.PubMedCrossRefGoogle Scholar
  10. 10.
    Mark TL, Swait J. Using stated preference and revealed preference modeling to evaluate prescribing decisions. Health Econ. 2004;13(6):563–73.PubMedCrossRefGoogle Scholar
  11. 11.
    Hole AR. A comparison of approaches to estimating confidence intervals for willingness to pay measures. Health Econ. 2007;16(8):827–40.PubMedCrossRefGoogle Scholar
  12. 12.
    Swait J, Adamowicz W. Choice environment, market complexity, and consumer behavior: a theoretical and empirical approach for incorporating decision complexity into models of consumer choice. Organ Behav Hum Decis Process. 2001;86(2):141–67.CrossRefGoogle Scholar
  13. 13.
    Fiebig DG, Keane MP, Louviere JJ, Wasi N. The generalized multinomial logit model: accounting for scale and coefficient heterogeneity. Mark Sci. 2010;29(3):393–421.CrossRefGoogle Scholar
  14. 14.
    Louviere JJ, Carson RT, Ainslie A, Cameron TA, DeShazo JR, Hensher D, et al. Dissecting the random component of utility. Mark Lett. 2002;13:177–93.CrossRefGoogle Scholar
  15. 15.
    Louviere JJ, Eagle T. Confound it! That pesky little scale constant messes up our convenient assumptions. In: Proceedings of 2006 sawtooth software conference. Sequem: Sawtooth Software; 2006. p. 211–28.Google Scholar
  16. 16.
    Louviere JJ, Street D, Burgess L, Wasi N, Islam T, Marley AAJ. Modeling the choices of individuals decision makers by combining efficient choice experiment designs with extra preference information. J Choice Model. 2008;1(1):128–63.CrossRefGoogle Scholar
  17. 17.
    Meyer RJ, Louviere JJ. Formal choice models of informal choices: what choice modelling research can (and can’t) learn from behavioral theory. Rev Mark Res. 2007;4:3–32.CrossRefGoogle Scholar
  18. 18.
    Knox SA, Viney RC, Gu Y, Hole AR, Fiebig DG, Street DJ, et al. The effect of adverse information and positive promotion on women’s preferences for prescribed contraceptive products. Soc Sci Med. 2013;83:70–80.PubMedCrossRefGoogle Scholar
  19. 19.
    Ryan M, Gerard K. Using discrete choice experiments to value health care programmes: current practice and future research reflections. Appl Health Econ Health Policy. 2003;2(1):55–64.PubMedGoogle Scholar
  20. 20.
    de Bekker-Grob EW, Ryan M, Gerard K. Discrete choice experiments in health economics: a review of the literature. Health Econ. 2012;21(2):145–72.PubMedCrossRefGoogle Scholar
  21. 21.
    Hall J, Kenny P, King M, Louviere J, Viney R, Yeoh A. Using stated preference discrete choice modelling to evaluate the introduction of varicella vaccination. Health Econ. 2002;11(5):457–65.PubMedCrossRefGoogle Scholar
  22. 22.
    Maddala T, Phillips KA, Reed Johnson F. An experiment on simplifying conjoint analysis designs for measuring preferences. Health Econ. 2003;12(12):1035–47.PubMedCrossRefGoogle Scholar
  23. 23.
    Ozdemir S, Mohamed AF, Johnson FR, Hauber AB. Who pays attention in stated-choice surveys? Health Econ. 2010;19(1):111–8.PubMedGoogle Scholar
  24. 24.
    Ryan M, Watson V. Comparing welfare estimates from payment card contingent valuation and discrete choice experiments. Health Econ. 2009;18(4):389–401.PubMedCrossRefGoogle Scholar
  25. 25.
    Telser H, Zweifel P. Measuring willingness-to-pay for risk reduction: an application of conjoint analysis. Health Econ. 2002;11(2):129–39.PubMedCrossRefGoogle Scholar
  26. 26.
    Reed Johnson F, Lancsar E, Marshall D, Kilambi V, Muhlbacher A, Regier DA, et al. Constructing experimental designs for discrete-choice experiments: report of the ISPOR Conjoint Analysis Experimental Design Good Research Practices Task Force. Value Health. 2013;16(1):3–13.PubMedCrossRefGoogle Scholar
  27. 27.
    Viney R, Lancsar E, Louviere J. Discrete choice experiments to measure consumer preferences for health and healthcare. Expert Rev Pharmacoecon Outcomes Res. 2002;2(4):319–26.PubMedCrossRefGoogle Scholar
  28. 28.
    Lancsar E, Savage E. Deriving welfare measures from discrete choice experiments: inconsistency between current methods and random utility and welfare theory. Health Econ. 2004;13(9):901–7.PubMedCrossRefGoogle Scholar
  29. 29.
    Dellaert BGC, Brazell JD, Louviere JJ. The effect of attribute variation on consumer choice consistency. Mark Lett. 1999;10(2):139–47.CrossRefGoogle Scholar
  30. 30.
    Keller KL, Staelin R. Effects of quality and quantity of information on decision effectiveness. J Consumer Res. 1987;14(2):200–13.CrossRefGoogle Scholar
  31. 31.
    de Bekker-Grob EW, Essink-Bot ML, Meerding WJ, Koes BW, Steyerberg EW. Preferences of GPs and patients for preventive osteoporosis drug treatment: a discrete-choice experiment. Pharmacoeconomics. 2009;27(3):211–9.PubMedCrossRefGoogle Scholar
  32. 32.
    de Bekker-Grob EW, Essink-Bot ML, Meerding WJ, Pols HA, Koes BW, Steyerberg EW. Patients’ preferences for osteoporosis drug treatment: a discrete choice experiment. Osteoporos Int. 2008;19(7):1029–37.PubMedCrossRefGoogle Scholar
  33. 33.
    de Bekker-Grob EW, Rose JM, Donkers B, Essink-Bot ML, Bangma CH, Steyerberg EW. Men’s preferences for prostate cancer screening: a discrete choice experiment. Br J Cancer. 2013;108(3):533–41.PubMedCrossRefGoogle Scholar
  34. 34.
    Daly A, Hess S, de Jong G. Calculating errors for measures derived from choice modelling estimates. Transp Res Part B. 2012;46(2):333–41.CrossRefGoogle Scholar
  35. 35.
    Hess S, Rose JM. Can scale and coefficient heterogeneity be separated in random coefficients models? Transportation. 2012;39(6):1225–39.CrossRefGoogle Scholar
  36. 36.
    Flynn TN, Louviere JJ, Peters TJ, Coast J. Using discrete choice experiments to understand preferences for quality of life: variance-scale heterogeneity matters. Soc Sci Med. 2010;70(12):1957–65.PubMedCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Esther W. de Bekker-Grob
    • 1
  • John M. Rose
    • 2
  • Michiel C. J. Bliemer
    • 2
  1. 1.Department of Public HealthErasmus MC, University Medical Centre RotterdamRotterdamThe Netherlands
  2. 2.The University of Sydney Business SchoolThe University of SydneySydneyAustralia

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