Multiple imputation (MI) inference handles missing data by imputing the missing values $m$ times, and then combining the results from the $m$ complete-data analyses. However, the existing method for combining likelihood ratio tests (LRTs) has multiple defects: (i) the combined test statistic can be negative, but its null distribution is approximated by an $F$-distribution; (ii) it is not invariant to re-parametrization; (iii) it fails to ensure monotonic power owing to its use of an inconsistent estimator of the fraction of missing information (FMI) under the alternative hypothesis; and (iv) it requires nontrivial access to the LRT statistic as a function of parameters instead of data sets. We show, using both theoretical derivations and empirical investigations, that essentially all of these problems can be straightforwardly addressed if we are willing to perform an additional LRT by stacking the $m$ completed data sets as one big completed data set. This enables users to implement the MI LRT without modifying the complete-data procedure. A particularly intriguing finding is that the FMI can be estimated consistently by an LRT statistic for testing whether the $m$ completed data sets can be regarded effectively as samples coming from a common model. Practical guidelines are provided based on an extensive comparison of existing MI tests. Issues related to nuisance parameters are also discussed.
翻译:多重估算(MI) 推断处理缺失的数据,方法是估算缺失的值为百万美元,然后将完整的数据分析结果合在一起,但是,合并概率比测试(LRTs)的现有方法存在多种缺陷:(一) 综合测试统计可能是负数,但其完全分布大约为美元分配额;(二) 重新校正并非易变性;(三) 无法确保单调能力,因为它使用一个不一致的估算器,在替代假设下对缺失信息部分的估算器(FMI)不一致;(四) 综合概率比测试(LRTs)的现有方法具有多种缺陷:(一) 综合测试统计数据可能是负数的,而不是数据集的功能。 我们通过理论推算和经验调查表明,如果我们愿意将已完成的美元数据集堆装成一个大完成的数据集,这些问题基本上都可以直接解决;(二) 这使用户能够在不修改完整数据程序的参数下实施MI LRT(FMI),特别令人惊奇地发现,将LRT统计作为参数的一种有效的比较方法,是否能够通过常规测试,从现有的样本中持续地估算出一个与FMI有关的数据。