Speaker: Hao Wang, PhD Candidate, Department of Statistics, Iowa State University

Title: A REML Approach for Variance Component Estimation in High-dimensional Linear Mixed-effects Models with Application to Heritability

Abstract: Linear mixed-effects models (LMMs) are widely used in many fields, including genetics and economics. With the influx of high-dimensional data, there are cases where we encounter high-dimensional fixed effects with a few random effects introduced by the experimental design. In such cases, statistical challenges arise for selecting fixed effects and estimating variance components in LMM analysis. During this talk, we first propose a REstricted Maximum Likelihood (REML) approach to estimate variance components with high-dimensional mixed-effects models. Our proposed approach utilizes LASSO to select fixed effects and get a working model, based on which REML is applied to estimate variance components. It is applicable to diverse settings in practice including clustered data. We prove that such REML estimators reserve appealing theoretical properties. Next, we apply a novel inference scheme to select fixed effects with transformed data using the estimated variance-covariance matrix. Simulation studies show that our inference using the estimated matrix performs comparable to the oracle case using the true variance-covariance matrix. Lastly, we propose to use high-dimensional LMMs to quantify heritability in plant breeding, where understanding the genetic basis of phenotypic traits is essential. We focus on studies employing complex designs, such as split-plot designs, and collecting rich environmental information, such as root-associated microbiomes. We demonstrate our proposed method provides more efficient heritability estimates using simulation studies and a real-world example.