Small-sample degrees of freedom with multiple imputation
Small-sample degrees of freedom with multiple imputation
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DOI：
10.1093/biomet/86.4.948
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发表时间：
1999-12-01
期刊：
影响因子：
2.7
通讯作者：
Rubin, DB
中科院分区：
文献类型：
--
作者：
Barnard, J;Rubin, DB
多重插补的一个吸引人的特征是将多个完整数据推断组合成最终推断的规则的简单性，重复插补推断（Rubin，1987）。该推断基于t分布，并在完整数据自由度v（com）为无穷大，但插补数量m为有限的假设下，从贝叶斯范式推导得出。当v（com）很小且缺失数据的比例很小时，t参考分布的重复插补自由度v（m）可能远大于v（com），这显然是不合适的。遵循贝叶斯范式，我们推导出一个调整的自由度，（v）在波浪线（m），具有以下三个性质：对于固定的m和估计的缺失信息的分数，（v）在波浪线（m）单调增加v（com）;（v）在波浪线（m）总是小于或等于v（com）;和（v）在波浪线（m）等于v（m）时，v（com）是无限的。一个小的模拟研究表明，当使用（v）而不是v（m）时，频率论性能上级。
An appealing feature of multiple imputation is the simplicity of the rules for combining the multiple complete-data inferences into a final inference, the repeated-imputation inference (Rubin, 1987). This inference is based on a t distribution and is derived from a Bayesian paradigm under the assumption that the complete-data degrees of freedom, v(com), are infinite, but the number of imputations, m, is finite. When v(com) is small and there is only a modest proportion of missing data, the calculated repeated-imputation degrees of freedom, v(m), for the t reference distribution can be much larger than v(com), which is clearly inappropriate. Following the Bayesian paradigm, we derive an adjusted degrees of freedom, (v) over tilde(m), with the following three properties: for fixed m and estimated fraction of missing information, (v) over tilde(m) monotonically increases in v(com); (v) over tilde(m) is always less than or equal to v(com); and (v) over tilde(m) equals v(m) when v(com) is infinite. A small simulation study demonstrates the superior frequentist performance when using (v) over tilde(m) rather than v(m).