MAXIMIZING HERITABILITY OF A LINEAR COMBINATION OF TRAITS

In 1971 Jones proposed an approximate procedure for finding that linea r combination of scores which has maximum heritability in a twin sampl e. I give an exact small-sample procedure. I point out two problems: s uch procedures can overoptimize the heritability by capitalizing on ch ance, and confidence intervals and significance tests are needed. I gi ve an approach using James-Stein shrinkage estimation and bootstrapped standard errors to address these problems. It appears that confidence intervals may be quite broad. To reduce the width of the confidence i ntervals, one can accept some small-sample bias in exchange for smalle r sampling errors. The James-Stein approach to estimating coefficients is used to achieve reduced confidence interval width. I illustrate wi th a computational example using personality data.