Multiple Improvements of Multiple Imputation Likelihood Ratio Tests

Multiple imputation (MI) inference handles missing data by imputing the values $m$ times, and then combining results from complete-data analyses. However, existing method for likelihood ratio tests (LRTs) has multiple defects: (i) combined test statistic can be negative, but its null distribution is approximated an $F$-distribution; (ii) it not invariant to re-parametrization; (iii) fails ensure monotonic power owing use of inconsistent estimator fraction information (FMI) under alternative hypothesis; (iv) requires nontrivial access LRT as a function parameters instead sets. We show, using both theoretical derivations empirical investigations, that essentially all these problems straightforwardly addressed if we are willing perform additional stacking completed sets one big set. This enables users implement MI without modifying procedure. A particularly intriguing finding FMI estimated consistently testing whether regarded effectively samples coming common model. Practical guidelines provided based on extensive comparison tests. Issues related nuisance also discussed.