Department of Meat and Animal Science, 1675 Observatory Dr., University of Wisconsin, 53706, Madison, WI, USA.
Theor Appl Genet. 1991 Jul;82(4):421-4. doi: 10.1007/BF00588594.
A bias correction was derived for the maximum likelihood estimator (MLE) of the intraclass correlation. The bias consisted of two parts: a correction from MLE to the analysis of variance estimator (ANOVA) and the bias of ANOVA. The total possible bias was always negative and depended upon both the degree of correlation and the design size and balance. The first part of the bias was an exact algebraic expression from MLE to ANOVA, and the corrected estimator by this part was ANOVA. It was also shown that the first correction term was equivalent to Fisher's reciprocal bias correction on hisZ scores. The total possible bias of MLE was large for small and moderate samples. Relative biases were larger for small parametric values and vice versa. To ensure a relative bias less than 10% assuming an intraclass correlation of 0.025, which is not unusual in most of the animal genetic studies, the total number of observations (N) should be not less than 500. From a design point of view, minimum bias occurred atn = 2, the minimum family size possible, underN fixed.
我们推导出了用于计算组内相关系数最大似然估计值(MLE)的偏差校正。该偏差由两部分组成:从 MLE 到方差分析估计值(ANOVA)的校正和 ANOVA 的偏差。总偏差始终为负,并且取决于相关性程度以及设计的大小和平衡性。偏差的第一部分是从 MLE 到 ANOVA 的精确代数表达式,通过该部分校正的估计值为 ANOVA。还表明,第一个校正项等同于 Fisher 在其 Z 分数上的倒数偏差校正。对于小样本和中等样本,MLE 的总偏差可能较大。对于较小的参数值,相对偏差较大,反之亦然。假设组内相关系数为 0.025,这在大多数动物遗传研究中并不罕见,为了确保相对偏差小于 10%,则在 N 固定的情况下,总观测数(N)不应小于 500。从设计角度来看,在 N 固定的情况下,最小的偏差出现在 n = 2,即最小的可能家庭规模。