  This simulation study evaluates the effectiveness of multiple imputation (MI)
techniques for multilevel data. It compares the performance of traditional
Multiple Imputation by Chained Equations (MICE) with tree-based methods such as
Chained Random Forests with Predictive Mean Matching and Extreme Gradient
Boosting. Adapted versions that include dummy variables for cluster membership
are also included for the tree-based methods. Methods are evaluated for
coefficient estimation bias, statistical power, and type I error rates on
simulated hierarchical data with different cluster sizes (25 and 50) and levels
of missingness (10\% and 50\%). Coefficients are estimated using random
intercept and random slope models. The results show that while MICE is
preferred for accurate rejection rates, Extreme Gradient Boosting is
advantageous for reducing bias. Furthermore, the study finds that bias levels
are similar across different cluster sizes, but rejection rates tend to be less
favorable with fewer clusters (lower power, higher type I error). In addition,
the inclusion of cluster dummies in tree-based methods improves estimation for
Level 1 variables, but is less effective for Level 2 variables. When data
become too complex and MICE is too slow, extreme gradient boosting is a good
alternative for hierarchical data.
  Keywords: Multiple imputation; multi-level data; MICE; missRanger; mixgb
