Bayesian Linear Mixed Models with Polygenic Effects

Abstract

We considered Bayesian estimation of polygenic effects, in particular heritability in relation to a class of linear mixed models implemented in R (R Core Team 2018). Our approach is applicable to both family-based and population-based studies in human genetics with which a genetic relationship matrix can be derived either from family structure or genome-wide data. Using a simulated and a real data, we demonstrate our implementation of the models in the generic statistical software systems JAGS (Plummer 2017) and Stan (Carpenter et al. 2017) as well as several R packages. In doing so, we have not only provided facilities in R linking standalone programs such as GCTA (Yang, Lee, Goddard, and Visscher 2011) and other packages in R but also addressed some technical issues in the analysis. Our experience with a host of general and special software systems will facilitate investigation into more complex models for both human and nonhuman genetics.