Faculty of Social and Behavioural Sciences, Department of Methodology and Statistics, Leiden University, PO Box 9500, 2300 RB, Leiden, The Netherlands.
Psychometrika. 2020 Mar;85(1):185-205. doi: 10.1007/s11336-020-09696-4. Epub 2020 Mar 11.
Whenever statistical analyses are applied to multiply imputed datasets, specific formulas are needed to combine the results into one overall analysis, also called combination rules. In the context of regression analysis, combination rules for the unstandardized regression coefficients, the t-tests of the regression coefficients, and the F-tests for testing [Formula: see text] for significance have long been established. However, there is still no general agreement on how to combine the point estimators of [Formula: see text] in multiple regression applied to multiply imputed datasets. Additionally, no combination rules for standardized regression coefficients and their confidence intervals seem to have been developed at all. In the current article, two sets of combination rules for the standardized regression coefficients and their confidence intervals are proposed, and their statistical properties are discussed. Additionally, two improved point estimators of [Formula: see text] in multiply imputed data are proposed, which in their computation use the pooled standardized regression coefficients. Simulations show that the proposed pooled standardized coefficients produce only small bias and that their 95% confidence intervals produce coverage close to the theoretical 95%. Furthermore, the simulations show that the newly proposed pooled estimates for [Formula: see text] are less biased than two earlier proposed pooled estimates.
无论何时对多重插补数据集进行统计分析，都需要特定的公式将结果合并为一个整体分析，也称为组合规则。在回归分析的背景下，对于未标准化的回归系数、回归系数的 t 检验以及用于检验 [公式：见正文] 显著性的 F 检验，其组合规则早已确立。然而，对于应用于多重插补数据集的多元回归中 [公式：见正文] 的点估计值如何进行组合，仍然没有普遍的共识。此外，似乎根本没有制定标准化回归系数及其置信区间的组合规则。在本文中，提出了两组标准化回归系数及其置信区间的组合规则，并讨论了它们的统计性质。此外，还提出了两种改进的多元插补数据中 [公式：见正文] 的点估计值，在计算过程中使用了合并的标准化回归系数。模拟结果表明，所提出的合并标准化系数仅产生较小的偏差，并且其 95%置信区间的覆盖接近理论的 95%。此外，模拟结果表明，新提出的 [公式：见正文] 的合并估计值比之前提出的两个合并估计值的偏差更小。
