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Implications of Errors in Survey Data: A Bayesian Model

Author

Listed:
  • Anil Gaba

    (INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France)

  • Robert L. Winkler

    (Fuqua School of Business, Duke University, Durham, North Carolina 27706 and INSEAD, Boulevard de Constance, 77305 Fontainebleau Cedex, France)

Abstract

Data from surveys often include errors, and such errors can have a serious effect on inferences about behavior or perceptions. In this paper a model is developed for making inferences based on dichotomous survey data with possible errors. A likelihood analysis reveals an identification problem, which can be avoided when a Bayesian approach is taken. The model is illustrated with purchase recall data from two previous studies, and the analysis shows that errors can have a significant impact on inferences about behavior. Ignoring such errors leads to point estimates that are systematically too high in many cases and to interval estimates that are unrealistically narrow. The effective amount of information in the survey data is reduced dramatically by the presence of errors. These results have important implications for the use and value of survey data in marketing and in many other areas.

Suggested Citation

  • Anil Gaba & Robert L. Winkler, 1992. "Implications of Errors in Survey Data: A Bayesian Model," Management Science, INFORMS, vol. 38(7), pages 913-925, July.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:7:p:913-925
    DOI: 10.1287/mnsc.38.7.913
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    Citations

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    Cited by:

    1. Rahardja, Dewi & Young, Dean M., 2011. "Likelihood-based confidence intervals for the risk ratio using double sampling with over-reported binary data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 813-823, January.
    2. Rahardja, Dewi & Young, Dean M., 2010. "Credible sets for risk ratios in over-reported two-sample binomial data using the double-sampling scheme," Computational Statistics & Data Analysis, Elsevier, vol. 54(5), pages 1281-1287, May.
    3. Boese, Doyle H. & Young, Dean M. & Stamey, James D., 2006. "Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3369-3385, August.
    4. Quinino, R. C. & Lee Ho, L., 2004. "Repetitive tests as an economic alternative procedure to control attributes with diagnosis errors," European Journal of Operational Research, Elsevier, vol. 155(1), pages 209-225, May.
    5. Al-Kandari Noriah M. & Lahiri Partha, 2016. "Prediction of a Function of Misclassified Binary Data," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 429-447, September.
    6. Noriah M. Al-Kandari & Partha Lahiri, 2016. "Prediction Of A Function Of Misclassified Binary Data," Statistics in Transition New Series, Polish Statistical Association, vol. 17(3), pages 429-447, September.
    7. Klein, Barbara D., 2001. "Detecting errors in data: clarification of the impact of base rate expectations and incentives," Omega, Elsevier, vol. 29(5), pages 391-404, October.
    8. Ashley Ling & El Hamidi Hay & Samuel E Aggrey & Romdhane Rekaya, 2018. "A Bayesian approach for analysis of ordered categorical responses subject to misclassification," PLOS ONE, Public Library of Science, vol. 13(12), pages 1-17, December.
    9. Partha Lahiri & Noriah M. Al-Kandari, 2016. "Prediction of a Function of Misclassified Binary Data," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 17(3), pages 429-447, September.
    10. M. Ruiz & F. J. Giron & C. J. Perez & J. Martin & C. Rojano, 2008. "A Bayesian model for multinomial sampling with misclassified data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 369-382.
    11. Bollinger, Christopher R. & van Hasselt, Martijn, 2017. "A Bayesian analysis of binary misclassification," Economics Letters, Elsevier, vol. 156(C), pages 68-73.
    12. T. Pham-Gia & N. Turkhan, 2005. "Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions," Statistical Papers, Springer, vol. 46(2), pages 247-266, April.
    13. Martijn van Hasselt & Christopher R. Bollinger & Jeremy W. Bray, 2022. "A Bayesian approach to account for misclassification in prevalence and trend estimation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 351-367, March.
    14. Anil Gaba & W. Kip Viscusi, 1998. "Differences in Subjective Risk Thresholds: Worker Groups as an Example," Management Science, INFORMS, vol. 44(6), pages 801-811, June.

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