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

Zvi Gilula, Robert E. McCulloch, Yaacov Ritov, Oleg Urminsky

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)325-357
Number of pages33
JournalQuantitative Marketing and Economics
Issue number3
StatePublished - Sep 15 2019


  • Categorical conversion
  • Conditional entropy
  • Mixture models
  • Ordinal attitudinal scales
  • Stochastic ordering

ASJC Scopus subject areas

  • Economics, Econometrics and Finance (miscellaneous)
  • Marketing


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