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Activity Number: 582 - Statistical Methods for Functional Data
Type: Contributed
Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
Sponsor: Section on Nonparametric Statistics
Abstract #324022
Title: Nested Hierarchical Functional Data Modeling and Inference for the Analysis of Functional Plant Phenotypes
Author(s): Yuhang Xu* and Yehua Li and Dan Nettleton
Companies: University of Nebraska-Lincoln and Iowa State University and Iowa State University
Keywords: Functional data analysis ; Akaike information criterion ; Generalized likelihood ratio test ; Penalized splines ; Principal components ; Permutation test

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.

Authors who are presenting talks have a * after their name.

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