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

Zvi Gilula (), Robert E. McCulloch (), Yaacov Ritov () and Oleg Urminsky ()
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Zvi Gilula: Hebrew University
Robert E. McCulloch: Arizona State University
Yaacov Ritov: University of Michigan
Oleg Urminsky: University of Chicago Booth School of Business

Quantitative Marketing and Economics (QME), 2019, vol. 17, issue 3, No 3, 325-357

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11129-019-09209-3

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