Some Transformations of Scale and the Estimation of Genetic Parameters from Daughter-Dam Regression

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Abstract
Some transformations of scale made to eliminate non-normality in the distribution of a trait, to reduce heterogeneity among error variances, and to maximize the regression of offspring on parent are considered with reference to the estimation of heritability and genetic correlation from parent-offspring regression. For certain non-empirical transformations it can be shown theoretically that changes of scale are unlikely to alter appreciably the estimates of such parameters. The construction of the maximizing transformation is given in some detail. In an example several transformations are derived for the trait fat percentage deviation from herd-year-season average in dairy cattle. When these scales are used in daughter-dam regression analysis, the differences among the various estimates of the genetic parameters are small and are not considered of practical significance in applied breeding programs.