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.

中文翻译：

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将估计的育种值从观测值转换为概率尺度：如何提高分类数据分析的效率


阈值模型通常用于分类数据的遗传分析，例如产犊的难易程度。责任量表中的解决方案很容易转化为概率;因此，估计的育种值被公布为表达主要兴趣类别的概率，并且是行业的黄金标准，因为它们易于解释和用于选择。但是，由于阈值模型涉及非线性方程和概率函数，因此实现这种方法很复杂。挑战包括计算时间长和收敛问题，而包含基因组数据加剧了这些问题。线性模型是克服这些挑战的替代方案。使用线性模型计算的估计育种值与阈值模型计算的估计育种值高度相关 （≥0.96）;但是，缺乏从观测到概率尺度的转换限制了线性模型的使用。本研究的目的是提出从观察到的到概率量表的转换，类似于从责任到概率量表的转换。我们评估了计算时间、峰值内存使用、估计育种值之间的相关性以及线性和阈值模型的估计遗传趋势。在系谱中有 11M 动物和近 965k 基因分型动物的情况下，线性模型的收敛速度比阈值模型快 5× 小时（32 小时对 145 小时），峰值内存使用相同（189 GB）。提出的转换提供了来自线性和阈值模型的高度相关的概率。来自线性和阈值模型的直接（母系）估计育种值与转换为概率的相关性为 ≥0.99 （0.97） 对于系谱中的所有动物，有/没有后代记录的公牛，或有表型记录的动物;因此，估计的遗传趋势是相似的，表明采用线性模型而不是阈值模型的育种计划没有遗传进展的损失。此外，与阈值模型相比，线性模型将计算时间缩短了 5 倍;这使得每周的遗传评估成为可能，并为使用分类性状的多性状模型来提高选择效果提供了可能性。