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A study into mechanisms of attitudinal scale conversion: A randomized stochastic ordering approach
Quantitative Marketing and Economics ( IF 1.480 ) Pub Date : 2019-01-25 , DOI: 10.1007/s11129-019-09209-3
Zvi Gilula , Robert E. McCulloch , Yaacov Ritov , Oleg Urminsky

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.

中文翻译:

态度尺度转换机制的研究:随机随机排序方法

本文考虑了方法上的挑战,即如何将在一个量表上测得的分类态度评分(如满意度)转换为在不同范围内另一个量表上测得的分类态度评分。在营销咨询中,这已成为一个日益严重的问题,并且常见的解决方案似乎太少而且太肤浅。提出了一种新的规模换算方法,并在全面研究中进行了测试。在基本方面,该方法被证明是相关且最佳的。新方法基于一种名为最小条件熵的新颖算法,它使用两个量表中每个量表的响应的边际分布来产生唯一的联合双变量分布。在此联合分布中,条件分布遵循随机顺序,该顺序在类别中是单调的,并具有最大化两个基础边际规模之间的相关性的相关最佳属性。我们展示了如何使用这种联合分布来建立规模转换的机制。我们同时使用常驻和贝叶斯方法来导出转换机制的混合模型,并讨论与基础模型相关的一些推断方面。这些模型可以纳入受访者的背景变量。进行了独特的观察实验,以实证验证所提出的建模方法。获得了强有力的验证证据。
更新日期:2019-01-25
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