Relative Efficiencies of Heritability Estimates Based on Regression of Offspring on Parent

The problem of optimal estimation of the coefficient of regression of offspring on parent (in the sense of minimum variance), when the number of progeny per parent is arbitrary, was completely solved by Kempthorne and Tandon [1953]. Prior to this paper, two methods were (and still are) commonly used: (1) the regression of the phenotypic mean of all offspring of a given parent on the parent's record; (2) the regression of offspring on parent, in which the parent's record is repeated for each of its progeny. Kempthorne and Tandon's technique, which they refer to as (3) the weighted regression technique, assigns weights to the progeny means which are functions of the number of progeny and a guessed value of a correlation coefficient p between deviations from regression associated with two progeny of the same parent. The difficulty here lies in the fact that p is unknown. The success of the general technique depends upon guessing p accurately. Presumably if the guessed value of p is close to p, the weighted technique is close to optimal. The precise effect of a poor guess for p does not seem to be known. The purposes of this paper are (1) to investigate the nature and magnitude of the correlation coefficient p, and (2) to compare the efficiencies of the various techniques with respect to data from a population of poultry.