FSEM: Functional Structural Equation Models for Twin Functional Data

ABSTRACT

The aim of this article 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. Supplementary materials for this article are available online.

KEYWORDS:

• Covariance function
• Genetic and environmental effects
• Weighted likelihood ratio test

Additional information

Funding

The wok of Dr. H. Zhu was partially supported by NIH grants MH086633 and MH092335, NSF grants SES-1357666 and DMS-1407655, a grant from the Cancer Prevention Research Institute of Texas, and the endowed Bao-Shan Jing Professorship in Diagnostic Imaging. The work of Dr. R. Song was partially supported by NSF-DMS-1555244 and NCI P01 CA142538. The work of Dr. J.H. Gilmore was partially supported by NIH grants MH111944, MH070890, and HD053000. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH or any other funding agency.