Transforming estimated breeding values from observed to probability scale: how to make categorical data analyses more efficient.

Threshold models are often used in genetic analysis of categorical data, such as calving ease. Solutions in the liability scale are easily transformed into probabilities; therefore, estimated breeding values are published as the probability of expressing the category of main interest and are the industry's gold standard because they are easy to interpret and use for selection. However, because threshold models involve nonlinear equations and probability functions, implementing such a method is complex. Challenges include long computing time and convergence issues, intensified by including genomic data. Linear models are an alternative to overcome those challenges. Estimated breeding values computed using linear models are highly correlated (≥0.96) with those from threshold models; however, the lack of a transformation from the observed to the probability scale limits the use of linear models. The objective of this study was to propose transformations from observed to probability scale analogous to the transformation from liability to probability scale. We assessed computing time, peak memory use, correlations between estimated breeding values, and estimated genetic trends from linear and threshold models. With 11M animals in the pedigree and almost 965k genotyped animals, linear models were 5× faster to converge than threshold models (32 vs. 145 h), and peak memory use was the same (189 GB). The transformations proposed provided highly correlated probabilities from linear and threshold models. Correlations between direct (maternal) estimated breeding values from linear and threshold models and transformed to probabilities were ≥0.99 (0.97) for all animals in the pedigree, sires with/without progeny records, or animals with phenotypic records; therefore, estimated genetic trends were analogous, suggesting no loss of genetic progress in breeding programs that would adopt linear instead of threshold models. Furthermore, linear models reduced computing time by 5-fold compared to the threshold models; this enables weekly genetic evaluations and opens the possibility of using multi-trait models for categorical traits to improve selection effectiveness.