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

• Published in: Quantitative marketing and economics 2019-09, Vol.17 (3), p.325-357
• Main Authors: Gilula, Zvi, McCulloch, Robert E., Ritov, Yaacov, Urminsky, Oleg
• Format: Article
• Language: English
• Subjects: Business and Management; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Finance; Insurance; Management; Marketing; Statistics for Business
• ISSN: 1570-7156; 1573-711X
• DOI: 10.1007/s11129-019-09209-3

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.