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A study into mechanisms of attitudinal scale conversion: A randomized stochastic ordering approach

Author

Listed:
  • Zvi Gilula

    (Hebrew University)

  • Robert E. McCulloch

    (Arizona State University)

  • Yaacov Ritov

    (University of Michigan)

  • Oleg Urminsky

    (University of Chicago Booth School of Business)

Abstract

This paper considers the methodological challenge of how to convert categorical attitudinal scores (like satisfaction) measured on one scale to a categorical attitudinal score measured on another scale with a different range. This is becoming a growing issue in marketing consulting and the common available solutions seem too few and too superficial. A new methodology for scale conversion is proposed, and tested in a comprehensive study. This methodology is shown to be both relevant and optimal in fundamental aspects. The new methodology is based on a novel algorithm named minimum conditional entropy, that uses the marginal distributions of the responses on each of the two scales to produce a unique joint bivariate distribution. In this joint distribution, the conditional distributions follow a stochastic order that is monotone in the categories and has the relevant optimal property of maximizing the correlation between the two underlying marginal scales. We show how such a joint distribution can be used to build a mechanism for scale conversion. We use both a frequentist and a Bayesian approach to derive mixture models for conversion mechanisms, and discuss some inferential aspects associated with the underlying models. These models can incorporate background variables of the respondents. A unique observational experiment is conducted that empirically validates the proposed modeling approach. Strong evidence of validation is obtained.

Suggested Citation

  • Zvi Gilula & Robert E. McCulloch & Yaacov Ritov & Oleg Urminsky, 2019. "A study into mechanisms of attitudinal scale conversion: A randomized stochastic ordering approach," Quantitative Marketing and Economics (QME), Springer, vol. 17(3), pages 325-357, September.
    • Handle: RePEc:kap:qmktec:v:17:y:2019:i:3:d:10.1007_s11129-019-09209-3
    DOI: 10.1007/s11129-019-09209-3
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    References listed on IDEAS

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    1. Dolnicar, Sara & Grün, Bettina, 2013. "“Translating” between survey answer formats," Journal of Business Research, Elsevier, vol. 66(9), pages 1298-1306.
    2. Michael Evans & Zvi Gilula & Irwin Guttman, 2012. "Conversion of ordinal attitudinal scales: An inferential Bayesian approach," Quantitative Marketing and Economics (QME), Springer, vol. 10(3), pages 283-304, September.
    3. Zvi Gilula & Robert McCulloch, 2013. "Multi level categorical data fusion using partially fused data," Quantitative Marketing and Economics (QME), Springer, vol. 11(3), pages 353-377, September.
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