Improving REML estimates of genetic parameters through penalties on correlation matrices

Penalized REML estimation can substantially reduce sampling variation in estimates of covariance matrices, and yield estimates of genetic parameters closer to population values than standard analyses. A number of suitable penalties based on prior distributions of correlation matrices from the Bayesian literature are described, and a simulation study is presented demonstrating their efficacy. Results show that reductions of 'loss' in estimates of the genetic covariance matrix, a conglomerate of sampling variance and bias, well over 50% are readily obtained for multivariate analyses of small samples. Default settings for a mild degree of penalization are proposed, which make such analyses suitable for routine use without increasing computational requirements.