Department of Animal Sciences, University of Wisconsin, Madison, Wisconsin 53706, USA.
Genet Sel Evol. 2010 Jan 25;42(1):1. doi: 10.1186/1297-9686-42-1.
The use of structural equation models for the analysis of recursive and simultaneous relationships between phenotypes has become more popular recently. The aim of this paper is to illustrate how these models can be applied in animal breeding to achieve parameterizations of different levels of complexity and, more specifically, to model phenotypic recursion between three calving traits: gestation length (GL), calving difficulty (CD) and stillbirth (SB). All recursive models considered here postulate heterogeneous recursive relationships between GL and liabilities to CD and SB, and between liability to CD and liability to SB, depending on categories of GL phenotype.
Four models were compared in terms of goodness of fit and predictive ability: 1) standard mixed model (SMM), a model with unstructured (co)variance matrices; 2) recursive mixed model 1 (RMM1), assuming that residual correlations are due to the recursive relationships between phenotypes; 3) RMM2, assuming that correlations between residuals and contemporary groups are due to recursive relationships between phenotypes; and 4) RMM3, postulating that the correlations between genetic effects, contemporary groups and residuals are due to recursive relationships between phenotypes.
For all the RMM considered, the estimates of the structural coefficients were similar. Results revealed a nonlinear relationship between GL and the liabilities both to CD and to SB, and a linear relationship between the liabilities to CD and SB.Differences in terms of goodness of fit and predictive ability of the models considered were negligible, suggesting that RMM3 is plausible.
The applications examined in this study suggest the plausibility of a nonlinear recursive effect from GL onto CD and SB. Also, the fact that the most restrictive model RMM3, which assumes that the only cause of correlation is phenotypic recursion, performs as well as the others indicates that the phenotypic recursion may be an important cause of the observed patterns of genetic and environmental correlations.
最近，使用结构方程模型分析表型之间的递归和同时关系变得越来越流行。本文的目的是说明如何在动物育种中应用这些模型，以实现不同复杂程度的参数化，更具体地说，是要对三个分娩性状（妊娠期、分娩难度和死产）之间的表型递归进行建模。 这里考虑的所有递归模型都假设 GL 和 CD 与 SB 的易感性之间以及 CD 的易感性与 SB 的易感性之间存在异质的递归关系，具体取决于 GL 表型的类别。
从拟合优度和预测能力方面比较了四种模型：1）标准混合模型（SMM），一种具有非结构（协）方差矩阵的模型；2）递归混合模型 1（RMM1），假设残差相关是由于表型之间的递归关系引起的；3）RMM2，假设残差与当代群体之间的相关性是由于表型之间的递归关系引起的；4）RMM3，假设遗传效应、当代群体和残差之间的相关性是由于表型之间的递归关系引起的。
对于所有考虑的 RMM，结构系数的估计值相似。结果表明，GL 与 CD 和 SB 的易感性之间存在非线性关系，而 CD 和 SB 之间存在线性关系。所考虑模型的拟合优度和预测能力差异可以忽略不计，这表明 RMM3 是合理的。
本研究中的应用表明 GL 对 CD 和 SB 的非线性递归效应是合理的。此外，最具限制性的模型 RMM3 假设相关性的唯一原因是表型递归，而其表现与其他模型一样，这表明表型递归可能是观察到遗传和环境相关性模式的重要原因。
