Regularized principal components of heritability

In family studies with multiple continuous phenotypes, heritability can be conveniently evaluated through the so-called principal-component of heredity (PCH, for short; Ott and Rabinowitz in Hum Hered 49:106-111, 1999). Estimation of the PCH, however, is notoriously difficult when entertaining a large collection of phenotypes which naturally arises in dealing with modern genomic data such as those from expression QTL studies. In this paper, we propose a regularized PCH method to specifically address such challenges. We show through both theoretical studies and data examples that the proposed method can accurately assess the heritability of a large collection of phenotypes.