# Behavior of the Linear Regression method to estimate bias and accuracies with correct and incorrect genetic evaluation models.J Dairy Sci 2020; 103(1):529-544JD

Bias in genetic evaluations has been a constant concern in animal genetics. The interest in this topic has increased in the last years, since many studies have detected overestimation (bias) in estimated breeding values (EBV). Detecting the existence of bias, and the realized accuracy of predictions, is therefore of importance, yet this is difficult when studying small data sets or breeds. In this study, we tested by simulation the recently presented method Linear Regression (LR) for estimation of bias, slope, and accuracy of pedigree EBV. The LR method computes statistics by comparing EBV from a data set containing old, partial information with EBV from a data set containing all information (old and new, a whole data set) for the same individuals. The method proposes an estimator for bias (Δpˆ), an estimator of slope (bpˆ), and 3 estimators related to accuracies: the ratio between accuracies [Formula: see text] the reliability of the partial data set (accp2ˆ), and the ratio of reliabilities (ρp,w2ˆ). We simulated a dairy scheme for low (0.10) and moderate (0.30) heritabilities. In both cases, we checked the behavior of the estimators for 3 scenarios: (1) when the evaluation model is the same as the model used to simulate the data; (2) when the evaluation model uses an incorrect heritability; and (3) when the data includes an environmental trend. For scenarios in which the evaluation model was correct, the LR method was capable of correctly estimating bias, slope, and accuracies, with better performance for higher heritability [i.e., corr(bp,bpˆ) was 0.45 for h2 = 0.10 and 0.59 for h2 = 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.

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*Journal of Dairy Science,*vol. 103, no. 1, 2020, pp. 529-544.

*J Dairy Sci*. 2020;103(1):529-544.

*Journal of Dairy Science,*

*103*(1), pp. 529-544. doi:10.3168/jds.2019-16603.

*J Dairy Sci.*2020;103(1):529-544. PubMed PMID: 31704008.