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Regression and Ordered Categorical Variables
Abstract
SUMMARY A general approach to regression modelling for ordered categorical response variables, y, is given, which is equally applicable to ordered and unordered y. The regressor variables xT = (x 1 ,…,xp) may be continuous or categorical. The method is based on the logistic family which contains a hierarchy of regression models, ranging from ordered to unordered models. Ordered properties of the former, the stereotype model, are established. The choice between models is made empirically on the basis of model fit. This is particularly important for assessed, ordered categorical response variables, where it is not obvious a priori whether or not the ordering is relevant to the regression relationship. Model simplification is investigated in terms of whether or not the response categories are distinguishable with respect to x. The models are fitted iteratively using the method of maximum likelihood. Examples are given.
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The OSM estimates the underlying scale by computing the expected probabilities of the categories based on potential covariates in the data.
“Thus, the OSMs estimate the underlying scale by computing the expected probabilities of the categories based on potential covariates in the data.”
From What is beautiful is still good: the attractiveness halo effect in the era of beauty filters (2024) · cites this paper as [57]
Categories with overlapping standard deviation intervals are merged into the same category in the OSM.
“Furthermore, categories with overlapping standard deviation intervals are merged into the same category.”
From What is beautiful is still good: the attractiveness halo effect in the era of beauty filters (2024) · cites this paper as [57]
The OSM estimates the distance between different categories based on the actual data instead of assuming that all categories are equidistant.
“The ϕk′s are interpreted as scores and help estimate the distance between different categories based on the actual data (ratings in our case) instead of assuming that all categories are equidistant.”
From What is beautiful is still good: the attractiveness halo effect in the era of beauty filters (2024) · cites this paper as [57]
The ordered stereotype model estimates the true spacing between points on the ordinal scale based on the data, resulting in a continuous transformed scale suitable for a linear model.
“The OSM estimates the true spacing between the points on the ordinal scale based on the data, thereby resulting in a transformed scale that is continuous and thus suitable for a linear model.”
From What is beautiful is still good: the attractiveness halo effect in the era of beauty filters (2024) · cites this paper as [57]
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Research works printed but not linked: 28
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Mixture-based clustering for the ordered stereotype model
Fernández, D., Arnold, R., & Pledger, S. (2016) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2014.11.004 · Cited by 39
Salas, L. A., Villanueva, C. M., Tajuddin, S. M., Amaral, A. F. S., Fernandez, A. F., Moore, L. E., Carrato, A., Tardón, A., Serra, C., García-Closas, R., et al. (2014) · Epigenetics · doi:10.4161/15592294.2014.983377 · Cited by 34
A method for ordinal outcomes: the ordered stereotype model
Fernandez, D., Liu, I., & Costilla, R. (2019) · International Journal of Methods in Psychiatric Research · doi:10.1002/mpr.1801 · Cited by 26
“This article focuses on the ordered stereotype model introduced by Anderson (1984), which is also flexible compared with the model with the proportional odds structure as a result of adding additional score parameters.”
BackgroundMethodWhat is beautiful is still good: the attractiveness halo effect in the era of beauty filters
Gulati, A., Martínez-Garcia, M., Fernández, D., Lozano, M. A., Lepri, B., & Oliver, N. (2024) · Royal Society Open Science · doi:10.1098/rsos.240882 · Cited by 21
Metadata
- Authors
- Anderson, J. A.
- Affiliations
- Newcastle University (GB)
- Corresponding author
- Anderson, J. A.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1984-09-01
- Volume
- 46
- Issue
- 1
- Pages
- 1-22
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W306181100
- Cited by
- 574
- References
- 0
- Citations by year
- 2026: 14 · 2025: 13 · 2024: 13 · 2023: 19 · 2022: 21 · 2021: 25 · 2020: 16 · 2019: 25 · 2018: 18 · 2017: 22 · 2016: 24 · 2015: 36 · 2014: 29 · 2013: 18 · 2012: 22
- FWCI
- 7.70
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- ordinal regression, model selection, model reduction, maximum likelihood estimation
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