A Mixture Distribution for Modelling Bivariate Ordinal Data

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aut.relation.journalStatistical Papers
dc.contributor.authorIp, Ryan HL
dc.contributor.authorWu, KYK
dc.date.accessioned2024-05-22T00:02:56Z
dc.date.available2024-05-22T00:02:56Z
dc.date.issued2024-05-20
dc.description.abstractOrdinal responses often arise from surveys which require respondents to rate items on a Likert scale. Since most surveys contain more than one question, the data collected are multivariate in nature, and the associations between different survey items are usually of considerable interest. In this paper, we focus on a mixture distribution, called the combination of uniform and binomial (CUB), under which each response is assumed to originate from either the respondent’s uncertainty or the actual feeling towards the survey item. We extend the CUB model to the bivariate case for modelling two correlated ordinal data without using copula-based approaches. The proposed model allows the associations between the unobserved uncertainty and feeling components of the variables to be estimated, a distinctive feature compared to previous attempts. This article describes the underlying logic and deals with both theoretical and practical aspects of the proposed model. In particular, we will show that the model is identifiable under a wide range of conditions. Practical inferential aspects such as parameter estimation, standard error calculations and hypothesis tests will be discussed through simulations and a real case study.
dc.identifier.citationStatistical Papers, ISSN: 0932-5026 (Print); 1613-9798 (Online), Springer. doi: 10.1007/s00362-024-01560-2
dc.identifier.doi10.1007/s00362-024-01560-2
dc.identifier.issn0932-5026
dc.identifier.issn1613-9798
dc.identifier.urihttp://hdl.handle.net/10292/17577
dc.publisherSpringer
dc.relation.urihttps://link.springer.com/article/10.1007/s00362-024-01560-2
dc.rightsOpen Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
dc.rights.accessrightsOpenAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.subject0104 Statistics
dc.subjectStatistics & Probability
dc.subject4905 Statistics
dc.titleA Mixture Distribution for Modelling Bivariate Ordinal Data
dc.typeJournal Article
pubs.elements-id553258
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