Estimation & Prediction

A new approach to scale breeding values from linear models to the liability scale: An application to binary traits in pigs

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Abstract

In commercial pig production, several economically important traits are recorded as binary phenotypes. Threshold models, based on the liability scale and its mapping to the observed scale, provide an accurate framework for binary traits but are computationally demanding and may face convergence issues. As a result, linear models are commonly used in genetic evaluations to predict genomic estimated breeding values (GEBV). Although computationally simpler, linear models do not allow a direct transformation of GEBV to the liability scale; thus, they lack a straightforward transformation to probabilities, which are the gold standard for selecting animals regarding binary traits. Therefore, a robust method is needed to approximate GEBV from the observed (linear model) to the liability scale before conversion into probabilities. A recently proposed method for this purpose showed limited success for traits with low prevalence (86%). Data were collected for five fitness traits (FT) with low (FT1 and FT2) and high prevalence (FT3, FT4, and FT5), including up to 233k phenotypes per trait. Genotypes for 23k SNPs were available for up to 204k animals. Variance components for each trait were estimated without genomic information, on the liability scale, using a threshold model as implemented in ASReml-R. For FT1 and FT2, a classical animal model was applied, for FT3, a repeatability animal model, and for FT4 and FT5, a maternal animal model. To obtain variance components on the observed scale, each component was multiplied by the square of the height of the ordinate of the standard normal distribution evaluated at the threshold. GEBV were predicted using single-step genomic best linear unbiased prediction with both single-trait linear and threshold models implemented in MiXBLUP 3.0. Both the previous and new approximations involved scaling GEBV to the observed scale using as a scaling factor: 1) the square root of the product of residual variance and the proportion of unexplained variance in the linear model, or 2) the height of the ordinate of the standard normal distribution evaluated at the threshold (new approximation). Spearman correlations, mean squared error (MSE), regression parameters, and distribution overlap were used to compare GEBV from linear and threshold models on the probability scale for both methods. Correlations between GEBV from threshold and linear models ranged from 0.94 (low prevalence) to 0.99 (high prevalence). While correlations were the same across approximations, MSE, regression parameters (Table 1) and distribution overlap improved with the new method. Therefore, the new approximation provides greater consistency and precision for large-scale evaluations using linear models for categorical traits with prevalences >2%.

Keywords: 2026

How to Cite:

de Oliveira Padilha, D., Leite, N., Hanenberg, E., van der Spek, D., Stevens, T., Bussiman, F., Lourenco, D., Misztal, I. & Hidalgo, J., (2026) “A new approach to scale breeding values from linear models to the liability scale: An application to binary traits in pigs”, World Congress on Genetics Applied to Livestock Production Digital Archive 2026(1): 2283425. doi: https://doi.org/10.31274/wcgalp.23497

Rights: 1