Department of Meat and Animal Science, University of Wisconsin, 1675 Observatory Drive, 53706, Madison, Wisconsin, USA.
Theor Appl Genet. 1992 Oct;85(1):79-88. doi: 10.1007/BF00223848.
At least two common practices exist when a negative variance component estimate is obtained, either setting it to zero or not reporting the estimate. The consequences of these practices are investigated in the context of the intraclass correlation estimation in terms of bias, variance and mean squared error (MSE). For the one-way analysis of variance random effects model and its extension to the common correlation model, we compare five estimators: analysis of variance (ANOVA), concentrated ANOVA, truncated ANOVA and two maximum likelihood-like (ML) estimators. For the balanced case, the exact bias and MSE are calculated via numerical integration of the exact sample distributions, while a Monte Carlo simulation study is conducted for the unbalanced case. The results indicate that the ANOVA estimator performs well except for designs with family size n = 2. The two ML estimators are generally poor, and the concentrated and truncated ANOVA estimators have some advantages over the ANOVA in terms of MSE. However, the large biases may make the concentrated and truncated ANOVA estimators objectionable when intraclass correlation (ϱ) is small. Bias should be a concern when a pooled estimate is obtained from the literature since ϱ<0.05 in many genetic studies.
当获得负方差分量估计值时，至少存在两种常见的做法，要么将其设置为零，要么不报告估计值。在类内相关估计的背景下，研究了这些做法对偏差、方差和均方误差（MSE）的影响。对于单向方差分析随机效应模型及其对常见相关模型的扩展，我们比较了五种估计器：方差分析（ANOVA）、集中方差分析、截断方差分析和两种最大似然似（ML）估计器。对于平衡情况，通过对精确样本分布的数值积分计算精确的偏差和 MSE，而对于不平衡情况，则进行蒙特卡罗模拟研究。结果表明，除了家庭大小 n=2 的设计外，方差分析估计器表现良好。两种 ML 估计器通常较差，集中和截断方差分析估计器在 MSE 方面相对于方差分析具有一些优势。然而，当类内相关（ρ）较小时，大的偏差可能会使集中和截断方差分析估计器变得不可接受。当从文献中获得 pooled 估计值时，应该关注偏差，因为在许多遗传研究中，ρ<0.05。
