IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v123y2018icp101-115.html
   My bibliography  Save this article

Model-based co-clustering for ordinal data

Author

Listed:
  • Jacques, Julien
  • Biernacki, Christophe

Abstract

A model-based co-clustering algorithm for ordinal data is presented. This algorithm relies on the latent block model embedding a probability distribution specific to ordinal data (the so-called BOS or Binary Ordinal Search distribution). Model inference relies on a Stochastic EM algorithm coupled with a Gibbs sampler, and the ICL-BIC criterion is used for selecting the number of co-clusters (or blocks). The main advantage of this ordinal dedicated co-clustering model is its parsimony, the interpretability of the co-cluster parameters (mode, precision) and the possibility to take into account missing data. Numerical experiments on simulated data show the efficiency of the inference strategy, and real data analyses illustrate the interest of the proposed procedure.

Suggested Citation

  • Jacques, Julien & Biernacki, Christophe, 2018. "Model-based co-clustering for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 101-115.
    • Handle: RePEc:eee:csdana:v:123:y:2018:i:c:p:101-115
    DOI: 10.1016/j.csda.2018.01.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318300239
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.01.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fernández, D. & Arnold, R. & Pledger, S., 2016. "Mixture-based clustering for the ordered stereotype model," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 46-75.
    2. Jan Schepers & Hans-Hermann Bock & Iven Mechelen, 2017. "Maximal Interaction Two-Mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 49-75, April.
    3. J. Jacques & C. Biernacki, 2010. "Extension of model-based classification for binary data when training and test populations differ," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 749-766.
    4. Eleni Matechou & Ivy Liu & Daniel Fernández & Miguel Farias & Bergljot Gjelsvik, 2016. "Biclustering Models for Two-Mode Ordinal Data," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 611-624, September.
    5. Hasnat, Md. Abul & Velcin, Julien & Bonnevay, Stephane & Jacques, Julien, 2017. "Evolutionary clustering for categorical data using parametric links among multinomial mixture models," Econometrics and Statistics, Elsevier, vol. 3(C), pages 141-159.
    6. D'Elia, Angela & Piccolo, Domenico, 2005. "A mixture model for preferences data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 49(3), pages 917-934, June.
    7. Pledger, Shirley & Arnold, Richard, 2014. "Multivariate methods using mixtures: Correspondence analysis, scaling and pattern-detection," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 241-261.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. C. Biernacki & J. Jacques & C. Keribin, 2023. "A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 332-381, July.
    2. Selosse, Margot & Jacques, Julien & Biernacki, Christophe, 2020. "Model-based co-clustering for mixed type data," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Goffinet, Etienne & Lebbah, Mustapha & Azzag, Hanane & Loïc, Giraldi & Coutant, Anthony, 2022. "Functional non-parametric latent block model: A multivariate time series clustering approach for autonomous driving validation," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    4. Arcagni, Alberto & Avellone, Alessandro & Fattore, Marco, 2022. "Complexity reduction and approximation of multidomain systems of partially ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    5. Alessandro Casa & Charles Bouveyron & Elena Erosheva & Giovanna Menardi, 2021. "Co-clustering of Time-Dependent Data via the Shape Invariant Model," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 626-649, October.
    6. M. P. B. Gallaugher & C. Biernacki & P. D. McNicholas, 2023. "Parameter-wise co-clustering for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1597-1619, September.
    7. Domenico Piccolo & Rosaria Simone, 2019. "Rejoinder to the discussion of “The class of cub models: statistical foundations, inferential issues and empirical evidence”," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 477-493, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Daniel Fernández & Richard Arnold & Shirley Pledger & Ivy Liu & Roy Costilla, 2019. "Finite mixture biclustering of discrete type multivariate data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 117-143, March.
    2. Christian Carmona & Luis Nieto-Barajas & Antonio Canale, 2019. "Model-based approach for household clustering with mixed scale variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(2), pages 559-583, June.
    3. Álvarez de Toledo, Pablo & Núñez, Fernando & Usabiaga, Carlos, 2018. "Matching and clustering in square contingency tables. Who matches with whom in the Spanish labour market," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 135-159.
    4. Tatjana Miljkovic & Daniel Fernández, 2018. "On Two Mixture-Based Clustering Approaches Used in Modeling an Insurance Portfolio," Risks, MDPI, vol. 6(2), pages 1-18, May.
    5. Roy Costilla & Ivy Liu & Richard Arnold & Daniel Fernández, 2019. "Bayesian model-based clustering for longitudinal ordinal data," Computational Statistics, Springer, vol. 34(3), pages 1015-1038, September.
    6. Daniel Fernández & Radim J. Sram & Miroslav Dostal & Anna Pastorkova & Hans Gmuender & Hyunok Choi, 2018. "Modeling Unobserved Heterogeneity in Susceptibility to Ambient Benzo[ a ]pyrene Concentration among Children with Allergic Asthma Using an Unsupervised Learning Algorithm," IJERPH, MDPI, vol. 15(1), pages 1-18, January.
    7. Gennaro Punzo & Rosalia Castellano & Mirko Buonocore, 2018. "Job Satisfaction in the “Big Four” of Europe: Reasoning Between Feeling and Uncertainty Through CUB Models," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 139(1), pages 205-236, August.
    8. Cicia, Gianni & Corduas, Marcella & Del Giudice, Teresa & Piccolo, Domenico, 2010. "Valuing Consumer Preferences with the CUB Model: A Case Study of Fair Trade Coffee," International Journal on Food System Dynamics, International Center for Management, Communication, and Research, vol. 1(1), pages 1-12.
    9. Manisera, Marica & Zuccolotto, Paola, 2014. "Modeling rating data with Nonlinear CUB models," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 100-118.
    10. Maria Iannario & Domenico Piccolo, 2016. "A comprehensive framework of regression models for ordinal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 233-252, August.
    11. Maria Iannario, 2010. "On the identifiability of a mixture model for ordinal data," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1), pages 87-94.
    12. Romina Gambacorta & Maria Iannario, 2012. "Statistical models for measuring job satisfaction," Temi di discussione (Economic working papers) 852, Bank of Italy, Economic Research and International Relations Area.
    13. Maria Iannario & Marica Manisera & Paola Zuccolotto, 2017. "Treatment of “don’t know” responses in the consumers’ perceptions about sustainability in the agri-food sector," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(2), pages 765-778, March.
    14. Scott D. Foster & Nicole A. Hill & Mitchell Lyons, 2017. "Ecological grouping of survey sites when sampling artefacts are present," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 1031-1047, November.
    15. 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.
    16. Sasanka Adikari & Norou Diawara, 2024. "Utility in Time Description in Priority Best–Worst Discrete Choice Models: An Empirical Evaluation Using Flynn’s Data," Stats, MDPI, vol. 7(1), pages 1-18, February.
    17. Zaheer Ahmed & Alberto Cassese & Gerard Breukelen & Jan Schepers, 2023. "E-ReMI: Extended Maximal Interaction Two-mode Clustering," Journal of Classification, Springer;The Classification Society, vol. 40(2), pages 298-331, July.
    18. Stefania Capecchi & Rosaria Simone, 2019. "A Proposal for a Model-Based Composite Indicator: Experience on Perceived Discrimination in Europe," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(1), pages 95-110, January.
    19. M. P. B. Gallaugher & C. Biernacki & P. D. McNicholas, 2023. "Parameter-wise co-clustering for high-dimensional data," Computational Statistics, Springer, vol. 38(3), pages 1597-1619, September.
    20. Paul Riverain & Simon Fossier & Mohamed Nadif, 2023. "Poisson degree corrected dynamic stochastic block model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 135-162, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:123:y:2018:i:c:p:101-115. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.