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Nested Hierarchical Functional Data Modeling and Inference for the Analysis of Functional Plant Phenotypes

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  • Yuhang Xu
  • Yehua Li
  • Dan Nettleton

Abstract

In a plant science Root Image Study, the process of seedling roots bending in response to gravity is recorded using digital cameras, and the bending rates are modeled as functional plant phenotype data. The functional phenotypes are collected from seeds representing a large variety of genotypes and have a three-level nested hierarchical structure, with seeds nested in groups nested in genotypes. The seeds are imaged on different days of the lunar cycle, and an important scientific question is whether there are lunar effects on root bending. We allow the mean function of the bending rate to depend on the lunar day and model the phenotypic variation between genotypes, groups of seeds imaged together, and individual seeds by hierarchical functional random effects. We estimate the covariance functions of the functional random effects by a fast penalized tensor product spline approach, perform multi-level functional principal component analysis (FPCA) using the best linear unbiased predictor of the principal component scores, and improve the efficiency of mean estimation by iterative decorrelation. We choose the number of principal components using a conditional Akaike information criterion and test the lunar day effect using generalized likelihood ratio test statistics based on the marginal and conditional likelihoods. We also propose a permutation procedure to evaluate the null distribution of the test statistics. Our simulation studies show that our model selection criterion selects the correct number of principal components with remarkably high frequency, and the likelihood-based tests based on FPCA have higher power than a test based on working independence. Supplementary materials for this article are available online.

Suggested Citation

  • Yuhang Xu & Yehua Li & Dan Nettleton, 2018. "Nested Hierarchical Functional Data Modeling and Inference for the Analysis of Functional Plant Phenotypes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 593-606, April.
  • Handle: RePEc:taf:jnlasa:v:113:y:2018:i:522:p:593-606
    DOI: 10.1080/01621459.2017.1366907
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    Cited by:

    1. Liu, Yanghui & Li, Yehua & Carroll, Raymond J. & Wang, Naisyin, 2022. "Predictive functional linear models with diverging number of semiparametric single-index interactions," Journal of Econometrics, Elsevier, vol. 230(2), pages 221-239.
    2. Weicheng Zhu & Sheng Xu & Catherine C. Liu & Yehua Li, 2023. "Minimax powerful functional analysis of covariance tests with application to longitudinal genome‐wide association studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 266-295, March.
    3. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    4. Haozhe Zhang & Yehua Li, 2020. "Unified Principal Component Analysis for Sparse and Dense Functional Data under Spatial Dependency," Papers 2006.13489, arXiv.org, revised Jun 2021.
    5. Wu Wang & Ying Sun & Huixia Judy Wang, 2023. "Latent group detection in functional partially linear regression models," Biometrics, The International Biometric Society, vol. 79(1), pages 280-291, March.
    6. Alexander S. Long & Brian J. Reich & Ana‐Maria Staicu & John Meitzen, 2023. "A nonparametric test of group distributional differences for hierarchically clustered functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3778-3791, December.

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