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Generalized infinite factorization models
[A latent factor linear mixed model for high-dimensional longitudinal data analysis]

Author

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  • L Schiavon
  • A Canale
  • D B Dunson

Abstract

SummaryFactorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. In practice, however, it can be challenging to infer the number of components and the relative impact of the different components. A popular idea is to include infinitely many components whose impact decreases with the component index. This article is motivated by two limitations of such existing methods: (i) lack of careful consideration of the within-component sparsity structure; and (ii) not accommodating grouped variables and other nonexchangeable structures. We propose a general class of infinite factorization models that address these limitations. Theoretical support is provided, practical gains are demonstrated in simulation studies, and an ecology application focusing on modelling bird species occurrence is discussed.

Suggested Citation

  • L Schiavon & A Canale & D B Dunson, 2022. "Generalized infinite factorization models [A latent factor linear mixed model for high-dimensional longitudinal data analysis]," Biometrika, Biometrika Trust, vol. 109(3), pages 817-835.
    • Handle: RePEc:oup:biomet:v:109:y:2022:i:3:p:817-835.
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
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    5. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2016. "Bayesian analysis of static and dynamic factor models: An ex-post approach towards the rotation problem," Journal of Econometrics, Elsevier, vol. 192(1), pages 190-206.
    6. Veronika Ročková & Edward I. George, 2016. "Fast Bayesian Factor Analysis via Automatic Rotations to Sparsity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1608-1622, October.
    7. Federico Ferrari & David B. Dunson, 2021. "Bayesian Factor Analysis for Inference on Interactions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1521-1532, July.
    8. Anirban Bhattacharya & Debdeep Pati & Natesh S. Pillai & David B. Dunson, 2015. "Dirichlet--Laplace Priors for Optimal Shrinkage," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1479-1490, December.
    9. repec:dau:papers:123456789/4648 is not listed on IDEAS
    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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    Cited by:

    1. Marco, Nicholas & Şentürk, Damla & Jeste, Shafali & DiStefano, Charlotte C. & Dickinson, Abigail & Telesca, Donatello, 2024. "Flexible regularized estimation in high-dimensional mixed membership models," Computational Statistics & Data Analysis, Elsevier, vol. 194(C).

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