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Bayesian function‐on‐function regression for multilevel functional data

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Listed:
  • Mark J. Meyer
  • Brent A. Coull
  • Francesco Versace
  • Paul Cinciripini
  • Jeffrey S. Morris

Abstract

Medical and public health research increasingly involves the collection of complex and high dimensional data. In particular, functional data—where the unit of observation is a curve or set of curves that are finely sampled over a grid—is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function‐on‐function regression model for repeatedly sampled functional data on a fine grid, presenting a simple model as well as a more extensive mixed model framework, and introducing various functional Bayesian inferential procedures that account for multiple testing. We examine these models via simulation and a data analysis with data from a study that used event‐related potentials to examine how the brain processes various types of images.

Suggested Citation

  • Mark J. Meyer & Brent A. Coull & Francesco Versace & Paul Cinciripini & Jeffrey S. Morris, 2015. "Bayesian function‐on‐function regression for multilevel functional data," Biometrics, The International Biometric Society, vol. 71(3), pages 563-574, September.
  • Handle: RePEc:bla:biomet:v:71:y:2015:i:3:p:563-574
    DOI: 10.1111/biom.12299
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    References listed on IDEAS

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    Cited by:

    1. Roy, Arkaprava & Ghosal, Subhashis, 2022. "Optimal Bayesian smoothing of functional observations over a large graph," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Qi, Xin & Luo, Ruiyan, 2018. "Function-on-function regression with thousands of predictive curves," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 51-66.
    3. Zhu, Hongxiao & Morris, Jeffrey S. & Wei, Fengrong & Cox, Dennis D., 2017. "Multivariate functional response regression, with application to fluorescence spectroscopy in a cervical pre-cancer study," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 88-101.
    4. Renat Sergazinov & Andrew Leroux & Erjia Cui & Ciprian Crainiceanu & R. Nisha Aurora & Naresh M. Punjabi & Irina Gaynanova, 2023. "A case study of glucose levels during sleep using multilevel fast function on scalar regression inference," Biometrics, The International Biometric Society, vol. 79(4), pages 3873-3882, December.

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