Title: Multiple Improvements of Multiple Imputation Likelihood Ratio Tests,
Abstract: 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.