A Practical Guide to Modern Imputation

TL;DR

Missing data imputation faces pitfalls that bias analyses; the authors advocate distributional, stochastic imputations and demonstrate benchmarking approaches to select methods. They promote iterative MICE variants (e.g., mice_cart, mice_rf) and knn within a MAR setting, and use energy-I-Score to rank methods that reproduce the imputation distribution. They show that RMSE/MAE can mislead in real data and propose bootstrap-based uncertainty quantification as a practical alternative to Rubin's rules. The paper provides concrete guidance, simulations (Gaussian and Uniform MAR), and a public codebase to help practitioners avoid common pitfalls and improve uncertainty assessment on imputed datasets.

Abstract

This guide based on recent papers should help researchers avoid some of the most common pitfalls of missing value imputation imputation.

Figures (8)

• Figure 1: Illustration of the mice imputation algorithm, originally from the fantastic video https://www.youtube.com/watch?v=zX-pacwVyvU, recreated and adapted using TikZ. Note that in accordance to Rule 1 in Section \ref{['Sec_1']}, the mice algorithm in each step learns a (conditional) distribution of one variable given all the others and depending on what method one chooses (linear regression with Gaussian errors, random forest, etc) a different method emerges.
• Figure 2: $\mathbf{X}$ is the assumed underlying full data, $\mathbf{M}$ is the vector of missing indicators and $\mathbf{X}^*$ arises when $\mathbf{M}$ is applied to $\mathbf{X}$. Thus each row of $\mathbf{X}$ (or $\mathbf{X}^*$) is an observation under a different pattern. Under missing completely at random (MCAR), no change is allowed. Under misisng at Random (MAR), the only constraint is that the distribution of $X_1, X_2 \mid X_3$ in the third pattern is the same as the unconditional one.
• Figure 4: 5000 observations of the bivariate Gaussian Example with around 50% MCAR missing values in $X_1$.(A) Original observations (observed and missing), (B) Imputation by fitting a regression model and imputing the prediction (mice_norm.predict), (C) Imputation by fitting a regression model and imputing by drawing from conditional Gaussian distribution (mice_norm). Figure taken from OneBenchmarktorulethemall.
• Figure 5: Imputation by learning from the part where $X_j$ is observed and imputing where it is missing, once using prediction (i.e. imputing by the estimated conditional expectation, the most likely value) on the left, and once using stochastic imputation (i.e. by drawing from the actually learned distribution) on the right.
• Figure 6: Result of the Uniform Example over 50 simulations, tested on missForest, knn, mice_drf, mice_rf, mice_cart. The vertical line represent the true value (0.1, in blue) and the true quantile of $X_1$ when considering only the observed values, without imputation ($-7 + \sqrt{49+15*0.1} \approx 0.106$, red). Methods are ordered by how closely the mean over the 50 replications is close to the true value of 0.1. See the file Section_2_QuantileTest.R.