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Splitting models for multivariate count data

Author

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  • Peyhardi, Jean
  • Fernique, Pierre
  • Durand, Jean-Baptiste

Abstract

We investigate the class of splitting distributions as the composition of a singular multivariate distribution and a univariate distribution. It will be shown that most common parametric count distributions (multinomial, negative multinomial, multivariate hypergeometric, multivariate negative hypergeometric, …) can be written as splitting distributions with separate parameters for both components, thus facilitating their interpretation, inference, the study of their probabilistic characteristics and their extensions to regression models. We highlight many probabilistic properties deriving from the compound aspect of splitting distributions and their underlying algebraic properties. Parameter inference and model selection are thus reduced to two separate problems, preserving time and space complexity of the base models. Based on this principle, we introduce several new distributions. In the case of multinomial splitting distributions, conditional independence and asymptotic normality properties for estimators are obtained. Mixtures of splitting regression models are used on a mango tree dataset in order to analyze the patchiness.

Suggested Citation

  • Peyhardi, Jean & Fernique, Pierre & Durand, Jean-Baptiste, 2021. "Splitting models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:jmvana:v:181:y:2021:i:c:s0047259x2030258x
    DOI: 10.1016/j.jmva.2020.104677
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    References listed on IDEAS

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    1. Claude Lefèvre & Stéphane Loisel, 2013. "On multiply monotone distributions, continuous or discrete, with applications," Post-Print hal-00750562, HAL.
    2. Stoltenberg, Emil Aas & Hjort, Nils Lid, 2020. "Multivariate estimation of Poisson parameters," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Jones, M.C. & Marchand, Éric, 2019. "Multivariate discrete distributions via sums and shares," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 83-93.
    4. Peyhardi, Jean & Fernique, Pierre, 2017. "Characterization of convolution splitting graphical models," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 59-64.
    5. Castañer, A. & Claramunt, M.M. & Lefèvre, C. & Loisel, S., 2015. "Discrete Schur-constant models," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 343-362.
    6. Fan Xia & Jun Chen & Wing Kam Fung & Hongzhe Li, 2013. "A Logistic Normal Multinomial Regression Model for Microbiome Compositional Data Analysis," Biometrics, The International Biometric Society, vol. 69(4), pages 1053-1063, December.
    7. J. Peyhardi & C. Trottier & Y. Guédon, 2015. "A new specification of generalized linear models for categorical responses," Biometrika, Biometrika Trust, vol. 102(4), pages 889-906.
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    Cited by:

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