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Mixture-based clustering for the ordered stereotype model

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  • Fernández, D.
  • Arnold, R.
  • Pledger, S.

Abstract

Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. Recently a group of likelihood-based finite mixture models for a data matrix with binary or count data, using basic Bernoulli or Poisson building blocks has been developed. This is extended and establishes likelihood-based multivariate methods for a data matrix with ordinal data which applies fuzzy clustering via finite mixtures to the ordered stereotype model. Model-fitting is performed using the expectation–maximization (EM) algorithm, and a fuzzy allocation of rows, columns, and rows and columns simultaneously to corresponding clusters is obtained. A simulation study is presented which includes a variety of scenarios in order to test the reliability of the proposed model. Finally, the results of the application of the model in two real data sets are shown.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:46-75
    DOI: 10.1016/j.csda.2014.11.004
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Daniel Fernández & Louise McMillan & Richard Arnold & Martin Spiess & Ivy Liu, 2022. "Goodness-of-Fit and Generalized Estimating Equation Methods for Ordinal Responses Based on the Stereotype Model," Stats, MDPI, vol. 5(2), pages 1-14, June.
    6. 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.
    7. Jacques, Julien & Biernacki, Christophe, 2018. "Model-based co-clustering for ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 101-115.
    8. 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.

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