Luo S, Song R, Styner M, Gilmore J H, Zhu H
Departments of Statistics, North Carolina State University, Cary, North Carolina, USA.
Department of Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA.
J Am Stat Assoc. 2019;114(525):344-357. doi: 10.1080/01621459.2017.1407773. Epub 2018 Jul 9.
The aim of this paper is to develop a novel class of functional structural equation models (FSEMs) for dissecting functional genetic and environmental effects on twin functional data, while characterizing the varying association between functional data and covariates of interest. We propose a three-stage estimation procedure to estimate varying coefficient functions for various covariates (e.g., gender) as well as three covariance operators for the genetic and environmental effects. We develop an inference procedure based on weighted likelihood ratio statistics to test the genetic/environmental effect at either a fixed location or a compact region. We also systematically carry out the theoretical analysis of the estimated varying functions, the weighted likelihood ratio statistics, and the estimated covariance operators. We conduct extensive Monte Carlo simulations to examine the finite-sample performance of the estimation and inference procedures. We apply the proposed FSEM to quantify the degree of genetic and environmental effects on twin white-matter tracts obtained from the UNC early brain development study.
本文的目的是开发一类新型的功能结构方程模型（FSEM），用于剖析功能遗传和环境对双胞胎功能数据的影响，同时刻画功能数据与感兴趣的协变量之间的变化关联。我们提出了一种三阶段估计程序，用于估计各种协变量（如性别）的变化系数函数以及遗传和环境效应的三个协方差算子。我们基于加权似然比统计量开发了一种推断程序，以检验在固定位置或紧凑区域的遗传/环境效应。我们还系统地对估计的变化函数、加权似然比统计量和估计的协方差算子进行了理论分析。我们进行了广泛的蒙特卡罗模拟，以检验估计和推断程序的有限样本性能。我们应用所提出的FSEM来量化遗传和环境对从UNC早期大脑发育研究中获得的双胞胎白质束的影响程度。
