miceSL: Super Learning Methods for mice

miceSL provides a unified super learning method for multiple imputation by chained equations (MICE).

It includes the local imputation approach of Laqueur et al., 2022 (superMICE) and the matching approach of Carpenito & Manjourides, 2022 (MISL) as special cases.

Installation

You can install the development version from GitHub:

# install.packages("devtools")
devtools::install_github("leofhp/miceSL")

Usage

The strategy and bootstrap arguments specify the sub-method to use:

• bootstrap:
  Boolean. Determines whether the super learner is trained on the full data (FALSE) or on a bootstrap sample in each iteration (TRUE).

• strategy:
  Character string specifying how imputed values for continuous variables are generated from the trained super learner model:

  • "localkernel" uses the local normal approximation of Laqueur et al. with a kernel-estimated variance.
  • "matching" uses the predictive mean matching approach of Carpenito & Manjourides.
  • "dirichlet" perturbs predictions by sampling new super learner weights from a Dirichlet distribution centered on the optimal weights.

Special cases:

• strategy = "localkernel", bootstrap = FALSE → superMICE
• strategy = "matching", bootstrap = TRUE → MISL

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Imputation for Different Variable Types

• strategy only affects continuous variables.
• Missing values in binary or categorical variables are always imputed by random draws from binomial or categorical distributions centered around the super learner predictions.
• The outcome_type argument controls this and can be "continuous", "binary", or "categorical".

Defaults:

• Numeric 0/1 or factor with two levels → "binary"
• Factor with more than two levels → "categorical"
• Otherwise → "continuous"

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Hyperparameters

Local kernel approach (strategy = "localkernel")

• kernel: Choice of "gaussian" (default), "uniform", or "triangular".
• bandwidth: Should match the data scale.
  • Laqueur et al. suggest setting it so that 0.7–2% of observed values lie within one standard deviation of the prediction under the Gaussian kernel.
  • Alternatively, they propose a jackknife selection procedure, which is called by passing a numeric vector of candidate bandwidths.
• Note: the bw.update argument from Laqueur et al. is not included due to the error-prone environment handling required for maintaining bandwidth configurations across iterations.

Dirichlet approach (strategy = "dirichlet")

• alpha: Scales the variance of the Dirichlet distribution used to perturb weights.
  • Larger alpha → lower variance of imputations.
  • Smaller alpha → higher variance.

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Super Learner Setup

The base learner set is specified via:

• continuous_learners
• binary_learners
• categorical_learners

Recommendations:

• Choose a more diverse learner set than the defaults.
• Any algorithm from SuperLearner or sl3 can be used, depending on sl_engine.

Further arguments:

• sl_engine:
  • Defaults to sl_engine = "SuperLearner", as it tends to have a faster runtime on a single core, which is the relevant performance measure since parallelization is recommended at the mice level (e.g., via mice::futuremice) rather than within the super learner itself.
  • However, outcome_type = "categorical" is currently only supported with sl3.
• cv_folds:
  • Number of cross-validation folds (default: 10). Can be reduced (e.g., to 5) to save computation. The impact of this is likely small since predictions are perturbed during imputation, reducing the risk of overfitting.

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Example

Here is a simple example using miceSL:

# Bivariate data (x, y) with missing values in x based on an MAR mechanism.
N <- 50
p <- 0.2
x <- rnorm(n = N, mean = 3, sd = 1)
y <- 10 + 2 * sin(x^2) - 0.05 * exp(x) - 0.5 * x +
  rnorm(n = N, mean = 0, sd = 0.5)
x[(runif(N) < (2 * p * pnorm(y, mean = mean(y), sd = sd(y))))] <- NA
df <- data.frame(x, y)

imps <- mice::mice(
  df, m = 50, maxit = 1, method = "sl", outcome_type = "continuous",
  continuous_learners = c("SL.mean", "SL.glm"), strategy = "localkernel",
  bootstrap = FALSE, bandwidth = 0.5, cv_folds = 5
)

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References

• Laqueur HS, Shev AB, Kagawa RMC. SuperMICE: An Ensemble Machine Learning Approach to Multiple Imputation by Chained Equations. American Journal of Epidemiology. 2022;191(3):516-525.
• Carpenito T, Manjourides J. MISL: Multiple imputation by super learning. Statistical Methods in Medical Research. 2022;31(10):1904-1915.