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A mixture model for ordinal variables measured on semantic differential scales

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  • Manisera, Marica
  • Zuccolotto, Paola

Abstract

Subjective perceptions and attitudes are usually measured by administering questionnaires with ordered response scales. Among them, a particular case are semantic differential scales, where the respondent has to declare his/her position between two bipolar adjectives. To model ordinal variables measured on semantic differential scales, a novel model is introduced as an extension in the framework of the CUB (Combination of discrete Uniform and shifted Binomial random variables) class of models. The proposed model addresses the analysis of ordinal variables measured on semantic differential scales. However, it is definitely well suited to all the rating scales that have a middle option that means indifference between two extremes. This is a circumstance that occurs in the main part of the most commonly used Likert scales. The proposal is based on a mixture of a discrete Uniform and a - linearly transformed - Multinomial random variable, so it is called CUM. Parameter estimation is carried out using the expectation-maximization algorithm, and the parameters can be represented in a triangular space with a ternary plot. A simulation study is carried out and, finally, applications on real data are examined in order to show limits and potentialities of the proposal.

Suggested Citation

  • Manisera, Marica & Zuccolotto, Paola, 2022. "A mixture model for ordinal variables measured on semantic differential scales," Econometrics and Statistics, Elsevier, vol. 22(C), pages 98-123.
    • Handle: RePEc:eee:ecosta:v:22:y:2022:i:c:p:98-123
    DOI: 10.1016/j.ecosta.2021.07.002
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    References listed on IDEAS

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    4. Rosaria Simone & Gerhard Tutz, 2018. "Modelling uncertainty and response styles in ordinal data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 224-245, August.
    5. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    6. Simone, Rosaria & Tutz, Gerhard & Iannario, Maria, 2020. "Subjective heterogeneity in response attitude for multivariate ordinal outcomes," Econometrics and Statistics, Elsevier, vol. 14(C), pages 145-158.
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