Recursive models are a category of structural equation models that propose a causal relationship between traits. These models are more parameterized than multiple trait models, and they require imposing restrictions on the parameter space to ensure statistical identification. Nevertheless, in certain situations, the likelihood of recursive models and multiple trait models are equivalent. Consequently, the estimates of variance components derived from the multiple trait mixed model can be converted into estimates under several recursive models through LDL′ or block-LDL′ transformations. The procedure was employed on a dataset comprising five traits (birth weight—BW, weight at 90 days—W90, weight at 210 days—W210, cold carcass weight—CCW and conformation—CON) from the Pirenaica beef cattle breed. These phenotypic records were unequally distributed among 149,029 individuals and had a high percentage of missing data. The pedigree used consisted of 343,753 individuals. A Bayesian approach involving a multiple-trait mixed model was applied using a Gibbs sampler. The variance components obtained at each iteration of the Gibbs sampler were subsequently used to estimate the variance components within three distinct recursive models. The LDL′ or block-LDL′ transformations applied to the variance component estimates achieved from a multiple trait mixed model enabled inference across multiple sets of recursive models, with the sole prerequisite of being likelihood equivalent. Furthermore, the aforementioned transformations simplify the handling of missing data when conducting inference within the realm of recursive models.

中文翻译：

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使用 LDL′ 变换的标准遗传模型和递归遗传模型之间的方差分量的等效性

递归模型是一类结构方程模型，提出特征之间的因果关系。这些模型比多性状模型参数化程度更高，并且需要对参数空间施加限制以确保统计识别。然而，在某些情况下，递归模型和多特征模型的可能性是相等的。因此，从多性状混合模型导出的方差分量的估计可以通过 LDL' 或 block-LDL' 变换转换为几个递归模型下的估计。该程序适用于包含 Pirenaica 肉牛品种的五个性状（出生体重 - BW、90 天体重 - W90、210 天体重 - W210、冷胴体重量 - CCW 和构象 - CON）的数据集。这些表型记录在 149,029 名个体中分布不均，并且缺失数据的比例很高。使用的谱系由 343,753 个人组成。使用吉布斯采样器应用涉及多特征混合模型的贝叶斯方法。随后使用吉布斯采样器每次迭代获得的方差分量来估计三个不同递归模型内的方差分量。将 LDL' 或块 LDL' 变换应用于从多特征混合模型获得的方差分量估计，可以跨多组递归模型进行推理，唯一的先决条件是似然等效。此外，上述转换简化了在递归模型领域内进行推理时丢失数据的处理。