Mixture-based clustering for the ordered stereotype model
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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 [58]
Section 5.2.2 describes combining two adjacent categories whose estimated score parameters were very close, and the simulation study says categories with equal score parameters could be merged for detecting clustering. The paper does not give overlapping standard-deviation intervals as the criterion, nor say that such categories are automatically merged. Page numbers are unavailable in our copy. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe 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 [58]
The Discussion (section 6; page unavailable) says the model estimates a new spacing of ordinal categories from the data. It does not say this is the true spacing or that the resulting scale is continuous and suitable for a linear model. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe 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 [58]
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 [58]
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Model-based co-clustering for ordinal data
Jacques, J., & Christophe Biernacki, A. (2018) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2018.01.014 · Cited by 71 · see citing works
A method for ordinal outcomes: the ordered stereotype model
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“Therefore, we could collapse them as a single response category (Fernández et al., 2016; Agresti, 2010).”
BackgroundCorneli, M., Bouveyron, C., & Latouche, P. (2020) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.2020.1739533 · Cited by 22 · see citing works
“In the last decades, several clustering algorithms for ordinal data have been introduced in the literature (D’Elia and Piccolo, 2005; Podani, 2006; Gouget, 2006; Jollois and Nadif, 2009; Giordan and Diana, 2011; Fernández et al., 2016; Ranalli and Rocci, 2016; Biernacki and Jacques, 2016).”
BackgroundWhat 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 · see citing works
“Section 2.3 describes the impact of the participants’ age and gender on the attractiveness halo effect by means of ordered stereotype models (OSM) [58] in conjunction with linear mixed models.”
InfluentialSelf-citationEcological Grouping of Survey Sites When Sampling Artefacts are Present
Foster, S. D., Hill, N. A., & Lyons, M. (2017) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.1111/rssc.12211 · Cited by 19 · see citing works
“…(c) perform biclustering where sampling sites and species are clustered simultaneously, but in the absence of covariates (Pledger and Arnold, 2014; Fernández et al., 2016) and (d) add spatial information (not general covariates) and utilized an application-specific likelihood (Pritchard et al.,…”
MethodCommon species distribution and environmental determinants in South American coastal plains
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Assigning scores for ordered categorical responses
Fernández, D., Liu, I., Costilla, R., & Gu, Y. (2019) · Journal of Applied Statistics · doi:10.1080/02664763.2019.1674790 · Cited by 16 · see citing works
“Recent examples of these are the application of a stereotype model in a case-control study by [3,4], the equivalence of posterior inference based on retrospective and prospective likelihoods by [20], a likelihood-based finite mixture biclustering method [15,16], a joint model of survival and longitudinal ordered data…”
BackgroundMethodInfluentialSelf-citationModel-based approach for household clustering with mixed scale variables
Carmona, C. U., Nieto-Barajas, L. E., & Canale, A. (2018) · Advances in Data Analysis and Classification · doi:10.1007/s11634-018-0313-6 · Cited by 16 · see citing works
“More recently, Fernández et al. (2016) used ordinal data in a model-based clustering, and Pledger and Arnold (2014) used mixtures in the correspondence analysis and scaling problems.”
MethodSimultaneous vegetation classification and mapping at large spatial scales
Lyons, M., Foster, S. D., & Keith, D. A. (2017) · Journal of Biogeography · doi:10.1111/jbi.13088 · Cited by 15 · see citing works
“Other data types could include species counts, biomass, or traits, from plants, as well as animals, fungi, etc. Ordinal data are not yet implemented, but recent work on this type of data (Fern andez et al., 2016) provides a good starting point.”
BackgroundArchetypal analysis for ordinal data
Fernández, D., Epifanio, I., & McMillan, L. (2021) · Information Sciences · doi:10.1016/j.ins.2021.07.095 · Cited by 13 · see citing works
“The parameter estimates may be calculated by the standard maximum likelihood (ML) method, by imposing the monotone non-decreasing constraint on / (2) through the reparametrization described in [34].”
MethodSelf-citationThe 2nd special issue on advances in mixture models
Böhning, D., Hennig, C. M., McLachlan, G. J., & McNicholas, P. D. (2013) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2013.10.010 · Cited by 13 · see citing works
Categorising Count Data into Ordinal Responses with Application to Ecological Communities
Fernández, D., & Pledger, S. (2015) · Journal of Agricultural Biological and Environmental Statistics · doi:10.1007/s13253-015-0240-3 · Cited by 12 · see citing works
Self-citationBiclustering Models for Two-Mode Ordinal Data
Matechou, E., Liu, I., Fernández, D., Farias, M., & Gjelsvik, B. (2016) · Psychometrika · doi:10.1007/s11336-016-9503-3 · Cited by 12 · see citing works
Self-citationA goodness‐of‐fit test for the ordered stereotype model
Fernández, D., & Liu, I. (2016) · Statistics in Medicine · doi:10.1002/sim.7002 · Cited by 11 · see citing works
Self-citationOn Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio
Miljkovic, T., & Fernández, D. (2018) · Risks · doi:10.3390/risks6020057 · Cited by 11 · see citing works
“The CWM method does not consider ordinal data; thus, we are also interested in the mixture-based clustering for OSM built to handle ordinal data previously proposed by Fernández et al. (2016).”
BackgroundMethodInfluentialSelf-citationModel selection for mixture-based clustering for ordinal data
Fernández, D., & Arnold, R. (2016) · Australian & New Zealand Journal of Statistics · doi:10.1111/anzs.12179 · Cited by 10 · see citing works
Self-citationde Toledo, P. Á., Hernández, F. N., & Usabiaga, C. (2018) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2018.05.012 · Cited by 10 · see citing works
Fernández, D., Šrám, R. J., Dostál, M., Pastorková, A., Gmuender, H., & Choi, H. (2018) · International Journal of Environmental Research and Public Health · doi:10.3390/ijerph15010106 · Cited by 7 · see citing works
Self-citationBayesian model-based clustering for longitudinal ordinal data
Costilla, R., Liu, I., Arnold, R., & Fernández, D. (2019) · Computational Statistics · doi:10.1007/s00180-019-00872-4 · Cited by 7 · see citing works
Self-citationGuilbault, E., Renner, I. W., Mahony, M. J., & Beh, E. J. (2021) · Ecology and Evolution · doi:10.1002/ece3.7411 · Cited by 7 · see citing works
“Mixture modeling is a common tool used to represent complex distributions and aims to identify different groups within a dataset while modeling heterogeneity (Fernández Martinez, 2015; Hui, 2016).”
MethodClustering longitudinal ordinal data via finite mixture of matrix-variate distributions
Amato, F., Jacques, J., & Prim‐Allaz, I. (2024) · Statistics and Computing · doi:10.1007/s11222-024-10390-z · Cited by 6 · see citing works
“In the clustering context we are interested in, the examples span from D’Elia and Piccolo (2005), that introduce the CUB model, later developed through the R package CUB (Iannario and Piccolo 2016), to Giordan and Diana (2011) and more recently Ranalli and Rocci (2016); Fernandez et al. (2016).”
Finite mixture biclustering of discrete type multivariate data
Fernández, D., Arnold, R., Pledger, S., Liu, I., & Costilla, R. (2018) · Advances in Data Analysis and Classification · doi:10.1007/s11634-018-0324-3 · Cited by 4 · see citing works
“Fernández and Arnold (2016) investigated the choice of the number of components most suitable for a given data set in the context of row clustering of ordinal data modelled by the ordered stereotype model (Fernández et al. 2016).”
BackgroundMethodInfluentialSelf-citationFernández, D., McMillan, L., Arnold, R., Spieß, M., & Liu, I. (2022) · Stats · doi:10.3390/stats5020030 · Cited by 3 · see citing works
“[35] because methods in other R packages do not enforce the ordinal nature of the responses.”
MethodSelf-citationMitani, A., Espin‐Garcia, O., Fernández, D., & Landsman, V. (2024) · Statistical Methods in Medical Research · doi:10.1177/09622802241282091 · Cited by 2 · see citing works
Self-citationRow mixture-based clustering with covariates for ordinal responses
Preedalikit, K., Fernández, D., Liu, I., McMillan, L., Ruscone, M. N., & Costilla, R. (2023) · Computational Statistics · doi:10.1007/s00180-023-01387-9 · Cited by 2 · see citing works
“Finally, to ensure that this approach does not affect any final estimates, we used the resulting maximum likelihood estimation of the complete data likelihood using the EM algorithm as starting points (Fernández et al. 2016) to numerically maximize the incomplete data log-likelihood (7).”
InfluentialSelf-citationModel-based goodness-of-fit tests for the ordered stereotype model
Fernández, D., Liu, I., Arnold, R., Nguyen, T. T. M., & Spieß, M. (2019) · Statistical Methods in Medical Research · doi:10.1177/0962280219864708 · Cited by 2 · see citing works
Self-citationRecursive clustering hematological data using mixture of exponential components
Suzdaleva, E., Nagy, I., & Petrouš, M. (2017) · International Conference on Intelligent Informatics and Biomedical Sciences (ICIIBMS) · doi:10.1109/iciibms.2017.8279700 · Cited by 2 · see citing works
“Studies dealing with the investigation of various distributions for the tasks of mixture-based clustering can be found in literature, for example, [14]–[16].”
BackgroundClustering and Classification in Fisheries
Fujita, Y. (2016) · doi:10.26686/wgtn.17019227 · Cited by 1 · see citing works
“Recently, Fernández et al. (2014) extended their approach to ordinal data.”
BackgroundMethodInfluentialPractical Initialization of Recursive Mixture-Based Clustering for Non-negative Data
Suzdaleva, E., & Nagy, I. (2019) · Lecture notes in electrical engineering · doi:10.1007/978-3-030-11292-9_34
Clustering and Classification in Fisheries
Fujita, Y. (2016) · doi:10.26686/wgtn.17019227.v1
Clustering repeated ordinal data: Model based approaches using finite mixtures
Monteagudo, R. K. C. (2017) · doi:10.26686/wgtn.17060354
The Third Special Issue on Advances in Mixture Models
Hinde, J., Ingrassia, S., Lin, T., & McNicholas, P. D. (2015) · Computational Statistics & Data Analysis · doi:10.1016/j.csda.2015.08.014
“In another application of biclustering, Fernández et al. (2016) consider ordinal responses and use finitemixtures of the stereotypemodel (Anderson, 1984).”
MethodClustering Categorical Data based on Finite Mixtures
Tran, K. T. (2022) · doi:10.26686/wgtn.19760143
Semi-supervised Model-Based Clustering for Ordinal Data
Cui, Y., McMillan, L., & Liu, I. (2023) · Communications in computer and information science · doi:10.1007/978-981-99-8696-5_3
Yee, T. W., Frigau, L., & Ma, C. (2025) · The Annals of Applied Statistics · doi:10.1214/25-aoas2065
Model-based Clustering Using Adjacent-Categories Logit Models via Finite-Mixtures for Ordinal Data
Cui, Y., Li, L., McMillan, L., Arnold, R., & Liu, I. (2025) · Journal of Classification · doi:10.1007/s00357-025-09524-3
Self-citation
- Authors
- Fernández, D., Arnold, R., & Pledger, S.
- Affiliations
- Victoria University of Wellington (NZ)
- Corresponding author
- Fernández, D.
- Venue
- Computational Statistics & Data Analysis
- Publisher
- Elsevier BV
- Published
- 2016-01
- Volume
- 93
- Pages
- 46-75
- ISSN
- 0167-9473 (ISSN-L)
- OpenAlex
- W2047306263
- Cited by
- 39
- References
- 79
- Citations by year
- 2025: 2 · 2024: 3 · 2023: 3 · 2022: 3 · 2021: 2 · 2020: 1 · 2019: 5 · 2018: 7 · 2017: 4 · 2016: 6 · 2015: 2 · 2013: 1
- FWCI
- 3.99
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Computational Statistics & Data Analysis (publishedVersion)
- UPCommons institutional repository (Universitat Politècnica de Catalunya) (acceptedVersion, cc-by-nc-nd)
- RePEc: Research Papers in Economics (submittedVersion)
- LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas) (submittedVersion, cc-by-nc-nd)
- ResearchArchive–Te Puna Rangahau (Victoria University of Wellington) (submittedVersion)
- Funders
- Victoria University of Wellington
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Physical Sciences › Computer Science › Artificial Intelligence › Advanced Clustering Algorithms Research
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Keywords
- mixture models, fuzzy clustering, ordinal data, dimensionality reduction, likelihood-based models, expectation-maximization algorithm
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