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Multivariate methods using mixtures: Correspondence analysis, scaling and pattern-detection

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  • Pledger, Shirley
  • Arnold, Richard

Abstract

Matrices of binary or count data are modelled under a unified statistical framework using finite mixtures to group the rows and/or columns. These likelihood-based one-mode and two-mode fuzzy clusterings provide maximum likelihood estimation of parameters and the options of using likelihood ratio tests or information criteria for model comparison. Geometric developments focused on pattern detection give likelihood-based analogues of various techniques in multivariate analysis, including multidimensional scaling, association analysis, ordination, correspondence analysis, and the construction of biplots. Illustrative examples demonstrate the effectiveness of these visualisations for identifying patterns of ecological significance (e.g. abrupt versus slow species turnover).

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  • 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.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:241-261
    DOI: 10.1016/j.csda.2013.05.013
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    References listed on IDEAS

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    5. Richard Arnold & Yu Hayakawa & Paul Yip, 2010. "Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension," Biometrics, The International Biometric Society, vol. 66(2), pages 644-655, June.
    6. O’Hagan, Adrian & Murphy, Thomas Brendan & Gormley, Isobel Claire, 2012. "Computational aspects of fitting mixture models via the expectation–maximization algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3843-3864.
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    Cited by:

    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. 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.
    3. 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.
    4. 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.
    5. D. Fernández & S. Pledger, 2016. "Categorising Count Data into Ordinal Responses with Application to Ecological Communities," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(2), pages 348-362, June.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. Jacques, Julien & Biernacki, Christophe, 2018. "Model-based co-clustering for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 101-115.
    11. Emilio Carrizosa & Vanesa Guerrero & Dolores Romero Morales, 2023. "On mathematical optimization for clustering categories in contingency tables," 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(2), pages 407-429, June.
    12. 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.
    13. Hui, Francis K.C., 2017. "Model-based simultaneous clustering and ordination of multivariate abundance data in ecology," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 1-10.

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