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Incorporating Clustering Techniques into GAMLSS

Author

Listed:
  • Thiago G. Ramires

    (Campus Apucarana, Universidade Tecnológica Federal do Paraná, Apucarana 86812-460, Brazil
    These authors contributed equally to this work.)

  • Luiz R. Nakamura

    (Departamento de Informática e Estatística, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil
    These authors contributed equally to this work.)

  • Ana J. Righetto

    (Alvaz Agritech, Londrina 86050-268, Brazil
    These authors contributed equally to this work.)

  • Andréa C. Konrath

    (Departamento de Informática e Estatística, Universidade Federal de Santa Catarina, Florianópolis 88040-900, Brazil
    These authors contributed equally to this work.)

  • Carlos A. B. Pereira

    (Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo 05508-090, Brazil
    These authors contributed equally to this work.)

Abstract

A method for statistical analysis of multimodal and/or highly distorted data is presented. The new methodology combines different clustering methods with the GAMLSS (generalized additive models for location, scale, and shape) framework, and is therefore called c-GAMLSS, for “clustering GAMLSS. ” In this new extended structure, a latent variable (cluster) is created to explain the response-variable (target). Any and all parameters of the distribution for the response variable can also be modeled by functions of the new covariate added to other available resources (features). The method of selecting resources to be used is carried out in stages, a step-based method. A simulation study considering multiple scenarios is presented to compare the c-GAMLSS method with existing Gaussian mixture models. We show by means of four different data applications that in cases where other authentic explanatory variables are or are not available, the c-GAMLSS structure outperforms mixture models, some recently developed complex distributions, cluster-weighted models, and a mixture-of-experts model. Even though we use simple distributions in our examples, other more sophisticated distributions can be used to explain the response variable.

Suggested Citation

  • Thiago G. Ramires & Luiz R. Nakamura & Ana J. Righetto & Andréa C. Konrath & Carlos A. B. Pereira, 2021. "Incorporating Clustering Techniques into GAMLSS," Stats, MDPI, vol. 4(4), pages 1-15, November.
    • Handle: RePEc:gam:jstats:v:4:y:2021:i:4:p:53-930:d:677377
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    References listed on IDEAS

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    1. Keefe Murphy & Thomas Brendan Murphy, 2020. "Gaussian parsimonious clustering models with covariates and a noise component," 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. 14(2), pages 293-325, June.
    2. Fionn Murtagh & Pierre Legendre, 2014. "Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion?," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 274-295, October.
    3. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    4. Stasinopoulos, D. Mikis & Rigby, Robert A., 2007. "Generalized Additive Models for Location Scale and Shape (GAMLSS) in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 23(i07).
    5. A. Azzalini & A.W. Bowman, 1990. "A Look at Some Data on the Old Faithful Geyser," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 39(3), pages 357-365, November.
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