title: A ridge penalized principal-components approach based on heritability for high-dimensional data.
abstract: OBJECTIVE
  To develop a ridge penalized principal-components approach based on heritability that can be applied to high-dimensional family data.
  
  
  METHODS
  The first principal component of heritability for a trait constellation is defined as a linear combination of traits that maximizes the heritability, which is equivalent to maximize the family-specific variation relative to the subject-specific variation. To analyze high-dimensional data and prevent overfitting, we propose a penalized principal-components approach based on heritability by adding a ridge penalty to the subject-specific variation. We choose the optimal regularization parameter by cross-validation.
  
  
  RESULTS
  The principal-components approach based on heritability with and without ridge penalty was compared to the usual principal-components analysis in four settings. The penalized principal-components of heritability analysis had substantially larger coefficients for the traits with genetic effect than for the traits with no genetic effect, while the non-regularized analysis failed to identify the genetic traits. In addition, linkage analysis on the combined traits showed that the power of the proposed methods was higher than the usual principal-components analysis and the non-regularized principal-components of heritability analysis.
  
  
  CONCLUSIONS
  The penalized principal-components approach based on heritability can effectively handle large number of traits with family structure and provide power gain for linkage analysis. The cross-validation procedure performs well in choosing optimal magnitude of penalty.
authors.affiliation: Department of Biostatistics, Mailman School of Public Health, Columbia University, New York, NY 10032, USA. yw2016@columbia.edu
authors.forename: Yuanjia
authors.initials: Y
authors.lastname: Wang
authors.forename: Yixin
authors.initials: Y
authors.lastname: Fang
authors.forename: Man
authors.initials: M
authors.lastname: Jin
mesh_terms: D008040:Genetic Linkage; D008957:Models, Genetic; D015233:Models, Statistical; D019655:Quantitative Trait, Heritable