Linear mixed models are widely used in ecological and biological applications, especially in genetic studies. Reliable estimation of variance components is crucial for using linear mixed models. However, standard methods, such as the restricted maximum likelihood (REML), are computationally inefficient and may be unstable with small samples. Other commonly used methods, such as the Haseman-Elston (HE) regression, may yield negative estimates of variances. Utilizing regularized estimation strategies, we propose the restricted Haseman-Elston (REHE) regression and REHE with resampling (reREHE) estimators, along with an inference framework for REHE, as fast and robust alternatives that provide non-negative estimates with comparable accuracy to REML. The merits of REHE are illustrated using real data and benchmark simulation studies.
Keywords: Genome-wide association study, Heritability study, Linear mixed model, Restricted Haseman-Elston regression, Variance component