REML法和Bayesian法对小样本不平衡单因素随机效应模型方差成分估计的模拟比较分析

A Comparison of REML and Bayesian Estimation of Variance Components for Unbalanced One-way Random Effects Models With Small Sample Sizes

目的比较限制性极大似然估计(REML)法和贝叶斯法(Bayesian)对小样本不平衡单因素随机效应模型方差成分估计的偏差和精密度,同时考虑在样本量的大小、单位的数量和单位内相关系数(ICC)的大小不同的情况下对方差成分估计的精确程度的影响。方法通过计算机模拟7组不同设计的数据集,用SAS软件MIXED模块进行方差成分估计。结果不同的设计中,REML法估计比Bayesian法估计更加接近真值,但Bayesian法对组间方差的区间估计更加精密。对于两种方法而言,样本和单位数量的增加,估计结果更加准确。组内方差的估计,比组间方差的估计更准确和精密。结论对小样本不平衡结构数据,当ICC为小或中等时,REML估计比Bayesian估计的偏差和均方误差要小,推荐使用。但是Bayesian法的区间估计比REML法的区间估计更加精密。

Objective To study how different designs affect the accuracy and precision of variance components estimation in small sample size unbalanced one-way random effects models. Methods Seven different design structures are simulated under various conditions with respect to sample size, number of random effects, and size of the intraclass correlation coefficient, and restricted maximum likelihood estimation （REML） is compared with Bayesian estimation of the variance components using PROC MIXED in SAS. Results REML estimates were more accurate compared to Bayesian estimates, but Bayesian interval estimates of the between - class variance were more precise than the REML interval estimates. For both methods, accuracy improved with larger sample sizes and more random effects. Estimation of the within - class variance was more ac- curate and precise compared to the estimation of the between - class variance. Conclusion For small sample unbalanced designs with small to moderate ICC values, REML estimation is recommended in terms of bias and mean squared error. Bayesian estimation is favored when considering interval estimation.