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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 325-357 |
| Number of pages | 33 |
| Journal | Quantitative Marketing and Economics |
| Volume | 17 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 15 2019 |
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Keywords
- Categorical conversion
- Conditional entropy
- Mixture models
- Ordinal attitudinal scales
- Stochastic ordering
ASJC Scopus subject areas
- Economics, Econometrics and Finance (miscellaneous)
- Marketing
Cite this
A study into mechanisms of attitudinal scale conversion : A randomized stochastic ordering approach. / Gilula, Zvi; McCulloch, Robert; Ritov, Yaacov; Urminsky, Oleg.
In: Quantitative Marketing and Economics, Vol. 17, No. 3, 15.09.2019, p. 325-357.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A study into mechanisms of attitudinal scale conversion
T2 - A randomized stochastic ordering approach
AU - Gilula, Zvi
AU - McCulloch, Robert
AU - Ritov, Yaacov
AU - Urminsky, Oleg
PY - 2019/9/15
Y1 - 2019/9/15
N2 - 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.
AB - 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.
KW - Categorical conversion
KW - Conditional entropy
KW - Mixture models
KW - Ordinal attitudinal scales
KW - Stochastic ordering
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U2 - 10.1007/s11129-019-09209-3
DO - 10.1007/s11129-019-09209-3
M3 - Article
VL - 17
SP - 325
EP - 357
JO - Quantitative Marketing and Economics
JF - Quantitative Marketing and Economics
SN - 1570-7156
IS - 3
ER -