Cantet R J C, Cappa E P
Departamento de Producción Animal Facultad de Agronomía, Universidad de Buenos Aires, Buenos Aires, Argentina.
J Anim Breed Genet. 2008 Dec;125(6):371-81. doi: 10.1111/j.1439-0388.2008.00743.x.
There is an increased interest in estimating the (co)variance components of additive animal models with direct and competition effects (AMC). However, some attempts to estimate the dispersion parameters in different animal species faced problems of convergence or inaccurate estimates when pen effects entered the model. We argue that the problem relates to lack of identifiability of the (co)variance components in some AMC. The check for identifiability of the dispersion parameters in mixed models with linear (co)variance structure requires that all the eigenvalues of the restricted maximum likelyhood information matrix (I(theta)) be positive. We show, by way of simple numerical examples, that the singularity of I(theta) is due to confounding between fixed pen effects and the additive competition effects (SBVs). It is also observed that setting pen effects as random does not always remedy the collinearity with SBVs. An alternative AMC is presented in which the incidence matrix of the SBVs can be written as a function of the 'intensity of competition' (IC) among animals in the same pen. Examples are presented in which the ICs are related to time. The distribution of families of full and half sibs across pens also plays a role in the identifiability and asymptotic variances of the (co)variance components.
人们对估计具有直接和竞争效应的加性动物模型（AMC）的（协）方差分量越来越感兴趣。然而，在不同动物物种中估计离散参数的一些尝试，当栏效应进入模型时，面临收敛问题或估计不准确的问题。我们认为，该问题与某些AMC中（协）方差分量缺乏可识别性有关。对于具有线性（协）方差结构的混合模型中离散参数的可识别性检查，要求限制最大似然信息矩阵（I(θ)）的所有特征值为正。我们通过简单的数值例子表明，I(θ)的奇异性是由于固定栏效应和加性竞争效应（SBVs）之间的混淆。还观察到将栏效应设为随机并不总是能纠正与SBVs的共线性。提出了一种替代的AMC，其中SBVs的关联矩阵可以写成同一栏中动物之间“竞争强度”（IC） 的函数。给出了IC与时间相关的例子。全同胞和半同胞家系在栏间的分布也对（协）方差分量的可识别性和渐近方差有影响。
