ctreeMI-package: ctreeMI: Conditional Inference Trees with Multiple Imputation

In ctreeMI: Conditional Inference Trees with Stacked Multiple Imputation

ctreeMI: Conditional Inference Trees with Multiple Imputation

Description

ctreeMI implements the stacked-imputation / Stack / M workflow for conditional inference trees (ctree) described in Sherlock et al. (2026).

The problem

Missing data are ubiquitous in applied research. Multiple imputation (MI) is the principled solution, but pooling results across imputations is straightforward only for linear-combination models (via Rubin's rules). Conditional inference trees (ctree) cannot be pooled across imputations because structurally different trees – which split on different variables at different nodes – define different subgroups, so the targets of inference are no longer aligned across imputations.

The solution

Stack the M imputed datasets vertically into one data frame of M x n rows, then fit a single ctree. The single tree is coherent and interpretable. The only problem: stacking inflates the nominal sample size by M, so test statistics at each node are similarly inflated and the tree over-splits.

Stack / M correction: divide each node-level test statistic by M, recompute its p-value from the chi-square reference distribution, reapply the multiplicity adjustment across candidate variables, and compress the tree bottom-up. This is not the same as dividing the significance threshold by M; the two rules coincide only at M = 1, and threshold rescaling under-corrects by an order of magnitude at M = 30. See ctree_stacked() for the derivation.

What the correction does and does not do

The correction removes the inflation attributable to the stacked sample size. It does not yield a calibrated node-level test: when the imputation model conditions on the outcome, which is recommended practice, the test rejects more often than its nominal level implies. The procedure recovers known structure and produces reproducible partitions well, but its node-level p-values are not error rates. See the "Node-level calibration" section of ctree_stacked().

Recommended workflow

Treat the tree as discovery and confirm it on independent data. discover_confirm() splits the sample, imputes each half separately, fits the tree on one half, and tests the resulting partition on the other with a procedure that pools across imputations by Rubin's rules and so has valid error control. split_holdout() and confirm_ctreeMI() expose the steps individually.

Main functions

ctree_stacked() fits the tree. It accepts a mids object from mice::mice(), a list of imputed data frames, or a plain data frame, and returns a fitted tree with full partykit compatibility. confirm_ctreeMI() tests a fitted tree's partition on held-out data. node_table() reports effective sample sizes per terminal node.

Citation

If you use ctreeMI, please cite both the package and the methodological paper:

Sherlock, P., Mansolf, M., Hofheimer, J., Hockett, C. W., O'Connor, T. G.,
  Roubinov, D., Graff, J. C., Lai, J.-S., Bush, N. R., Wright, R. J., &
  Chiu, Y.-H. M. (2026). Beyond linear risk: A machine learning approach
  to understanding perinatal depression in context.
  Multivariate Behavioral Research, 1-16.
  https://doi.org/10.1080/00273171.2026.2661244

The underlying ctree algorithm should also be cited:

Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased recursive
  partitioning: A conditional inference framework. Journal of
  Computational and Graphical Statistics, 15(3), 651-674.

Hothorn, T., & Zeileis, A. (2015). partykit: A modular toolkit for
  recursive partitioning in R. Journal of Machine Learning Research,
  16, 3905-3909.

Author(s)

Maintainer: Phillip Sherlock [e-mail] (ORCID)

See Also

Useful links:

• https://github.com/Phillip-Sherlock/ctreeMI

• Report bugs at https://github.com/Phillip-Sherlock/ctreeMI/issues

ctreeMI documentation built on Oct. 12, 2026, 5:08 p.m.