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

  • Zvi GilulaEmail author
  • Robert E. McCulloch
  • Yaacov Ritov
  • Oleg Urminsky
Article
  • 19 Downloads

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.

Keywords

Categorical conversion Conditional entropy Mixture models Ordinal attitudinal scales Stochastic ordering 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Zvi Gilula
    • 1
    Email author
  • Robert E. McCulloch
    • 2
  • Yaacov Ritov
    • 3
  • Oleg Urminsky
    • 4
  1. 1.Department of StatisticsHebrew UniversityJerusalemIsrael
  2. 2.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA
  3. 3.Department of StatisticsUniversity of MichiganAnn ArborUSA
  4. 4.University of Chicago Booth School of BusinessChicagoUSA

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