A mixture model for ordinal variables measured on semantic differential scales

Marica Manisera and Paola Zuccolotto

Econometrics and Statistics, 2022, vol. 22, issue C, 98-123

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.

Keywords: Categorical ordinal variables; CUB models; Multinomial distribution; Semantic differential (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S2452306221000782
Full text for ScienceDirect subscribers only. Contains open access articles

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:22:y:2022:i:c:p:98-123

DOI: 10.1016/j.ecosta.2021.07.002

Access Statistics for this article

Econometrics and Statistics is currently edited by E.J. Kontoghiorghes, H. Van Dijk and A.M. Colubi

More articles in Econometrics and Statistics from Elsevier
Bibliographic data for series maintained by Catherine Liu ().