Varona L, González-Recio O
Instituto Agroalimentario de Aragón (IA2), Facultad de Veterinaria, Universidad de Zaragoza, C/ Miguel Servet 177, 50013 Zaragoza, Spain.
Departamento de mejora genética animal, INIA-CSIC, Crta, de la Coruña km 7.5, 28040 Madrid, Spain.
J Dairy Sci. 2023 Apr;106(4):2198-2212. doi: 10.3168/jds.2022-22578. Epub 2023 Mar 2.
Structural equation models allow causal effects between 2 or more variables to be considered and can postulate unidirectional (recursive models; RM) or bidirectional (simultaneous models) causality between variables. This review evaluated the properties of RM in animal breeding and how to interpret the genetic parameters and the corresponding estimated breeding values. In many cases, RM and mixed multitrait models (MTM) are statistically equivalent, although subject to the assumption of variance-covariance matrices and restrictions imposed for achieving model identification. Inference under RM requires imposing some restrictions on the (co)variance matrix or on the location parameters. The estimates of the variance components and the breeding values can be transformed from RM to MTM, although the biological interpretation differs. In the MTM, the breeding values predict the full influence of the additive genetic effects on the traits and should be used for breeding purposes. In contrast, the RM breeding values express the additive genetic effect while holding the causal traits constant. The differences between the additive genetic effect in RM and MTM can be used to identify the genomic regions that affect the additive genetic variation of traits directly or causally mediated for another trait or traits. Furthermore, we presented some extensions of the RM that are useful for modeling quantitative traits with alternative assumptions. The equivalence of RM and MTM can be used to infer causal effects on sequentially expressed traits by manipulating the residual (co)variance matrix under the MTM. Further, RM can be implemented to analyze causality between traits that might differ among subgroups or within the parametric space of the independent traits. In addition, RM can be expanded to create models that introduce some degree of regularization in the recursive structure that aims to estimate a large number of recursive parameters. Finally, RM can be used in some cases for operational reasons, although there is no causality between traits.
结构方程模型允许考虑两个或多个变量之间的因果效应，并可以假定变量之间的单向（递归模型；RM）或双向（同时模型）因果关系。本综述评估了RM在动物育种中的特性，以及如何解释遗传参数和相应的估计育种值。在许多情况下，RM和混合多性状模型（MTM）在统计上是等效的，尽管要服从方差协方差矩阵的假设以及为实现模型识别而施加的限制。在RM下进行推断需要对（协）方差矩阵或位置参数施加一些限制。方差成分和育种值的估计可以从RM转换为MTM，尽管生物学解释有所不同。在MTM中，育种值预测加性遗传效应对性状的全部影响，应将其用于育种目的。相比之下，RM育种值在保持因果性状不变的情况下表达加性遗传效应。RM和MTM中加性遗传效应的差异可用于识别直接影响性状加性遗传变异或由另一个或多个性状因果介导的基因组区域。此外，我们还介绍了RM的一些扩展，这些扩展对于用替代假设对数量性状进行建模很有用。RM和MTM的等效性可用于通过操纵MTM下的残差（协）方差矩阵来推断对顺序表达性状的因果效应。此外，RM可用于分析亚组之间或独立性状参数空间内可能不同的性状之间的因果关系。此外，RM可以扩展以创建在递归结构中引入某种程度正则化的模型，旨在估计大量递归参数。最后，尽管性状之间没有因果关系，但在某些情况下出于操作原因可以使用RM。
