Behavior of the Linear Regression method to estimate bias and accuracies with correct and incorrect genetic evaluation models

Abstract

p p , ( ) was 0.45 for h 2 = 0.10 and 0.59 for h 2 = 0.30]. In cases of the use of incorrect heritabilities in the evaluation model, the bias was correctly estimated in direction but not in magnitude.In the same way, the magnitudes of bias and of slope were underestimated in scenarios with environmental trends in data, except for cases in which contemporary groups were random and greatly shrunken. In general, accuracies were well estimated in all scenarios. The LR method is capable of checking bias and accuracy in all cases, if the evaluation model is reasonably correct or robust, and its estimations are more precise with more information (e.g., high heritability). If the model uses an incorrect heritability or a hidden trend exists in the data, it is still possible to estimate the direction and existence of bias and slope but not always their magnitudes.

Bias and accuracy of dairy sheep evaluations using BLUP and SSGBLUP with metafounders and unknown parent groups

“…The LR method presents one estimator for the bias ( ), one estimator for the dispersion ( ) and four estimators related to the accuracies ( , , , ). The estimators are summarized below; for a deeper overview and properties of the estimators see [ 11 , 21 ].…”

“…In a general formulation, , where is the genetic variance of the group of individuals of interest. We use this more general formulation as in [ 21 ] instead of the formulation used in [ 11 ], because the latter is adequate only for a group of animals that represent the whole population after selection. In this work, we analyzed EBV of sets of contemporary young rams of the population, in other words highly-selected individuals, which decreases reliability [ 20 , 21 ].…”

“…We use this more general formulation as in [ 21 ] instead of the formulation used in [ 11 ], because the latter is adequate only for a group of animals that represent the whole population after selection. In this work, we analyzed EBV of sets of contemporary young rams of the population, in other words highly-selected individuals, which decreases reliability [ 20 , 21 ]. A difficulty associated to this estimator is the necessity of an estimation of the genetic variance of a group of individuals.…”

“…This estimator estimates the reliability as if there was no selection, as in [ 23 ], where is the genetic variance of the base population and is the genetic variance of the group of individuals of interest (see above). A short derivation of follows from [ 21 , 24 ], , so . The reliability that is unaffected by selection is leading to [ 23 ], where is the selected reliability.…”

“…Although there is no theoretical support for using the LR method across models [ 21 ], our objective was to check the consistency of models with each other, in the sense that a refinement of the model should not introduce unexpected changes in the evaluations. Otherwise, one of the models could possibly be quite wrong.…”