Graham John W, Olchowski Allison E, Gilreath Tamika D
Department of Biobehavioral Health, Penn State University, E-315 Health & Human Development Bldg., University Park, PA 16802, USA.
Prev Sci. 2007 Sep;8(3):206-13. doi: 10.1007/s11121-007-0070-9. Epub 2007 Jun 5.
Multiple imputation (MI) and full information maximum likelihood (FIML) are the two most common approaches to missing data analysis. In theory, MI and FIML are equivalent when identical models are tested using the same variables, and when m, the number of imputations performed with MI, approaches infinity. However, it is important to know how many imputations are necessary before MI and FIML are sufficiently equivalent in ways that are important to prevention scientists. MI theory suggests that small values of m, even on the order of three to five imputations, yield excellent results. Previous guidelines for sufficient m are based on relative efficiency, which involves the fraction of missing information (gamma) for the parameter being estimated, and m. In the present study, we used a Monte Carlo simulation to test MI models across several scenarios in which gamma and m were varied. Standard errors and p-values for the regression coefficient of interest varied as a function of m, but not at the same rate as relative efficiency. Most importantly, statistical power for small effect sizes diminished as m became smaller, and the rate of this power falloff was much greater than predicted by changes in relative efficiency. Based our findings, we recommend that researchers using MI should perform many more imputations than previously considered sufficient. These recommendations are based on gamma, and take into consideration one's tolerance for a preventable power falloff (compared to FIML) due to using too few imputations.
多重填补（MI）和全信息极大似然法（FIML）是缺失数据分析中最常用的两种方法。理论上，当使用相同变量测试相同模型，且多重填补（MI）执行的填补次数m趋近于无穷大时，MI和FIML是等效的。然而，对于预防科学家而言，了解在MI和FIML充分等效之前需要进行多少次填补非常重要。MI理论表明，即使m值较小，如三到五次填补，也能产生出色的结果。先前关于足够m值的指导方针基于相对效率，其中涉及所估计参数的缺失信息比例（γ）和m。在本研究中，我们使用蒙特卡洛模拟在γ和m变化的几种情况下测试MI模型。感兴趣的回归系数的标准误差和p值随m的变化而变化，但变化速率与相对效率不同。最重要的是，小效应量的统计功效随着m变小而降低，且这种功效下降的速率远大于相对效率变化所预测的速率。基于我们的研究结果，我们建议使用MI的研究人员应进行比先前认为足够的次数更多的填补。这些建议基于γ，并考虑到由于填补次数过少而导致的可预防的功效下降（与FIML相比）的容忍度。
