Adapting tree-based multiple imputation methods for multi-level data? A simulation study

TL;DR

This study evaluates novel tree-based imputation methods adapted for hierarchical data, demonstrating their advantages over traditional MICE especially at higher missingness rates and for level-1 variables.

Contribution

It introduces and assesses adapted tree-based imputation methods, specifically Chained Random Forests and Extreme Gradient Boosting with cluster dummies, for multilevel data.

Findings

Adapted boosting outperforms MICE at high missingness for level-1 variables.

MICE remains robust for level-2 variables at low missingness.

Tree-based methods show promise as alternatives to MICE in multilevel data.

Abstract

When data have a hierarchical structure, such as students nested within classrooms, ignoring dependencies between observations can compromise the validity of imputation procedures. Standard tree-based imputation methods implicitly assume independence between observations, limiting their applicability in multilevel data settings. Although Multivariate Imputation by Chained Equations (MICE) is widely used for hierarchical data, it has limitations, including sensitivity to model specification and computational complexity. Alternative tree-based approaches have shown promise for individual-level data, but remain largely unexplored for hierarchical contexts. In this simulation study, we systematically evaluate the performance of novel tree-based methods--Chained Random Forests and Extreme Gradient Boosting (mixgb)--explicitly adapted for multi-level data by incorporating dummy variables indicating cluster membership. We compare these tree-based methods and their adapted versions with traditional MICE imputation in terms of coefficient estimation bias, type I error rates and statistical power, under different cluster sizes, missingness mechanisms and missingness rates, using both random intercept and random slope data generation models. The results show that MICE provides robust and accurate inference for level 2 variables, especially at low missingness rates. However, the adapted boosting approach (mixgb with cluster dummies) consistently outperforms other methods for Level-1 variables at higher missingness rates (30%, 50%). For level 2 variables, while MICE retains better power at moderate missingness (30%), adapted boosting becomes superior at high missingness (50%), regardless of the missingness mechanism or cluster size. These findings highlight the potential of appropriately adapted tree-based imputation methods as effective alternatives to conventional MICE in multilevel data analyses.