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Abstract:
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In a plant science study, the process of seedling roots bending in response to gravity is recorded, and the bending rates are modeled as functional data. The data 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 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 PCA using the BLUP, and improve the efficiency of mean estimation by iterative decorrelation. We choose the number of principal components using a conditional AIC and test the lunar day effect using generalized likelihood ratio 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 have higher power than a test based on working independence.
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