Multiple imputation (MI) inference handles missing data by first properly imputing the missing values $m$ times, and then combining the $m$ analysis results from applying a complete-data procedure to each of the completed datasets. However, the existing method for combining likelihood ratio tests has multiple defects: (i) the combined test statistic can be negative in practice when the reference null distribution is a standard $F$ distribution; (ii) it is not invariant to re-parametrization; (iii) it fails to ensure monotonic power due to its use of an inconsistent estimator of the fraction of missing information (FMI) under the alternative hypothesis; and (iv) it requires non-trivial access to the likelihood ratio test statistic as a function of estimated parameters instead of datasets. This paper shows, via both theoretical derivations and empirical investigations, that essentially all of these problems can be straightforwardly addressed if we are willing to perform an additional likelihood ratio test by stacking the $m$ completed datasets as one big completed dataset. A particularly intriguing finding is that the FMI itself can be estimated consistently by a likelihood ratio statistic for testing whether the $m$ completed datasets produced by MI can be regarded effectively as samples coming from a common model. Practical guidelines are provided based on an extensive comparison of existing MI tests.
翻译:多重估算 (MI) 推断处理缺失的数据,先正确估算缺失值,然后对每个已完成的数据集应用完整数据程序,得出分析结果,然后将美元的分析结果合并起来。不过,合并概率比测试的现有方法存在多种缺陷:(一) 当参考无效分布为标准美元美元分布时,综合测试统计在实践中可能是负面的;(二) 重新校正并非易变;(三) 它无法确保单调能力,因为它在替代假设下使用一个不一致的缺失信息部分估计器(FMI),因此无法确保单调能力;(四) 它要求作为估计参数而不是数据集的函数,对概率率测试统计进行非连带访问。 本文通过理论推算和实证调查表明,如果我们愿意将已完成的美元数据集堆叠成一个大完成的数据集来进行额外的可能性比率测试,这些问题基本上都可以直接得到解决。 特别令人怀疑的是,根据现有实际数据测试的模型测试,能否有效地将FMI本身的概率进行比较。