Analyzing Twin Data with Generalized Linear Mixed-Effects Models and Bayesian Computation

Abstract

To study the genetic and environmental influences on observable behavior, ACE (Additive genetic component, Common environmental component, Error) models are often used in the twin studies. Structural equation modeling (SEM) is the classic approach to fit ACE models. Despite the popularity of SEMs, a lack of "random effects predictions" (predicted effects of each individual) hinders the study of individual differences. Also SEM does not easily accommodate response distributions other than the Gaussian family. As an alternative, ACE models can be formulated and analyzed in a mixed-effects model framework with generalized linear mixed-effects models (GLMMs). It produces best linear unbiased predictions (BLUPs) of the random effects and easily accommodates the exponential family distributions and zero-inflated distributions. However, the standard statistical softwares for GLMMs are not tailored towards modeling the kinship dependencies such as those assumed in classic ACE models. Further the estimation methods are not optimal for ACE models, which often result in non-convergence and inaccurate statistical inference. I propose a novel framework for Bayesian analysis of twin data via GLMM. First, a reparameterization of the ACE model is used to circumvent the constraints in the standard software therefore allowing the covariance of random effects to be dependent on the covariates and/or non-linear constraints to be imposed on model parameters. Second, a fast and flexible Bayesian procedure via Hamiltonian Monte Carlo is used for parameter estimation, implemented in a customized R package. Simulation studies and real data applications were carried out to illustrate the merits of the proposed method and spotlight the syntax of the accompanying R package mcmctwin.