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Functional structural equation model

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  • Kuang‐Yao Lee
  • Lexin Li

Abstract

In this article, we introduce a functional structural equation model for estimating directional relations from multivariate functional data. We decouple the estimation into two major steps: directional order determination and selection through sparse functional regression. We first propose a score function at the linear operator level, and show that its minimization can recover the true directional order when the relation between each function and its parental functions is nonlinear. We then develop a sparse functional additive regression, where both the response and the multivariate predictors are functions and the regression relation is additive and nonlinear. We also propose strategies to speed up the computation and scale up our method. In theory, we establish the consistencies of order determination, sparse functional additive regression, and directed acyclic graph estimation, while allowing both the dimension of the Karhunen–Loéve expansion coefficients and the number of random functions to diverge with the sample size. We illustrate the efficacy of our method through simulations, and an application to brain effective connectivity analysis.

Suggested Citation

  • Kuang‐Yao Lee & Lexin Li, 2022. "Functional structural equation model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 600-629, April.
    • Handle: RePEc:bla:jorssb:v:84:y:2022:i:2:p:600-629
    DOI: 10.1111/rssb.12471
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    References listed on IDEAS

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    1. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
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    5. S. Luo & R. Song & M. Styner & J. H. Gilmore & H. Zhu, 2019. "FSEM: Functional Structural Equation Models for Twin Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 344-357, January.
    6. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
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    10. Fei Fu & Qing Zhou, 2013. "Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(501), pages 288-300, March.
    11. Ali Shojaie & George Michailidis, 2010. "Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs," Biometrika, Biometrika Trust, vol. 97(3), pages 519-538.
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    13. Bing Li & Hyonho Chun & Hongyu Zhao, 2014. "On an Additive Semigraphoid Model for Statistical Networks With Application to Pathway Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1188-1204, September.
    14. Kuang-Yao Lee & Bing Li & Hongyu Zhao, 2016. "Variable selection via additive conditional independence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1037-1055, November.
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    Cited by:

    1. Fangting Zhou & Kejun He & Kunbo Wang & Yanxun Xu & Yang Ni, 2023. "Functional Bayesian networks for discovering causality from multivariate functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3279-3293, December.

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