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′ 变换的标准和递归遗传模型之间的方差分量等效性


递归模型是一类结构方程模型，它提出了性状之间的因果关系。这些模型比多个特征模型参数化程度更高，并且它们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，递归模型和多重特征模型的可能性是相等的。因此，从多性状混合模型得出的方差分量的估计值可以通过 LDL′ 或 block-LDL′ 转换转换为多个递归模型下的估计值。该程序被用于一个数据集，该数据集包含来自 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 和体型结构 - CON）。这些表型记录在 149,029 个个体中分布不均，并且缺失数据的百分比很高。使用的系谱由 343,753 人组成。使用 Gibbs 采样器应用涉及多性状混合模型的贝叶斯方法。随后，在 Gibbs 采样器的每次迭代中获得的方差分量用于估计三个不同递归模型中的方差分量。应用于从多性状混合模型实现的方差分量估计的 LDL′ 或 block-LDL′ 转换支持跨多组递归模型进行推理，唯一的前提是似然等效。此外，上述转换简化了在递归模型领域内进行推理时对缺失数据的处理。