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Generalized partially linear models on Riemannian manifolds

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  • Amelia Simó
  • M. Victoria Ibáñez
  • Irene Epifanio
  • Vicent Gimeno

Abstract

We introduce generalized partially linear models with covariates on Riemannian manifolds. These models, like ordinary generalized linear models, are a generalization of partially linear models on Riemannian manifolds that allow for scalar response variables with error distribution models other than a normal distribution. Partially linear models are particularly useful when some of the covariates of the model are elements of a Riemannian manifold, because the curvature of these spaces makes it difficult to define parametric models. The model was developed to address an interesting application: the prediction of children's garment fit based on three‐dimensional scanning of their bodies. For this reason, we focus on logistic and ordinal models and on the important and difficult case where the Riemannian manifold is the three‐dimensional case of Kendall's shape space. An experimental study with a well‐known three‐dimensional database is carried out to check the goodness of the procedure. Finally, it is applied to a three‐dimensional database obtained from an anthropometric survey of the Spanish child population. A comparative study with related techniques is carried out.

Suggested Citation

  • Amelia Simó & M. Victoria Ibáñez & Irene Epifanio & Vicent Gimeno, 2020. "Generalized partially linear models on Riemannian manifolds," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(3), pages 641-661, June.
  • Handle: RePEc:bla:jorssc:v:69:y:2020:i:3:p:641-661
    DOI: 10.1111/rssc.12411
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    References listed on IDEAS

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    1. R. Thompson & R. J. Baker, 1981. "Composite Link Functions in Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 125-131, June.
    2. Cui, Xia & Lu, Ying & Peng, Heng, 2017. "Estimation of partially linear regression models under the partial consistency property," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 103-121.
    3. Irene Epifanio & María Victoria Ibáñez & Amelia Simó, 2018. "Archetypal shapes based on landmarks and extension to handle missing 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. 12(3), pages 705-735, September.
    4. Wenceslao Gonzalez-Manteiga & Guillermo Henry & Daniela Rodriguez, 2012. "Partly linear models on Riemannian manifolds," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1797-1809, April.
    5. Qian, Lianfen & Wang, Suojin, 2017. "Subject-wise empirical likelihood inference in partial linear models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 77-87.
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    Cited by:

    1. Meisam Moghimbeygi & Anahita Nodehi, 2022. "Multinomial Principal Component Logistic Regression on Shape Data," Journal of Classification, Springer;The Classification Society, vol. 39(3), pages 578-599, November.
    2. Ferrando, L. & Epifanio, I. & Ventura-Campos, N., 2021. "Ordinal classification of 3D brain structures by functional data analysis," Statistics & Probability Letters, Elsevier, vol. 179(C).

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