Replication materials for How Should Missing Data Be Handled When Fitting Conditional Inference Trees?

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Replication materials for the manuscript "How Should Missing Data Be Handled When Fitting Conditional Inference Trees?" (Sherlock). This archive contains the Monte Carlo simulation code and complete numerical results for a study comparing six approaches to handling missing data when fitting conditional inference trees (ctree; Hothorn, Hornik & Zeileis, 2006): listwise deletion, surrogate splits, missingness incorporated in attributes (MIA), single imputation, uncorrected stacking of multiply imputed datasets, and stacking with a sample-size correction (Stack/M). Simulation design Ten simulation studies spanning 189 conditions. Each dataset contained eight predictors — four signal-carrying (binary, continuous, five-level ordered, four-level unordered) and four pure-noise predictors matched type for type, so that splits on noise predictors index variable-selection bias by measurement type. Five data-generating processes (null, main effects, interaction, ordinal/nominal, weak signal) were crossed with three missingness mechanisms (MCAR, MAR, MNAR) at rates of 15%, 30% and 45%, across sample sizes from n = 250 to n = 25,000. Imputations were generated with MICE, with M = 30 throughout except in Study 5, which varies M from 5 to 50. Studies 8–10 repeat the comparison with predictors correlated through a latent Gaussian factor model. Studies 1–5, 8 and 9 used 500 replications per condition; Studies 6, 7 and 10 used 200. All six approaches are applied to the same generated data within each condition, so the comparison is paired. Recorded per replicate: spurious subgroup, recovery of the complete true structure, Brier score or MSE on an independently generated test set of 2,000 fully observed cases, terminal-node count, rows available to the approach, and whether a tree was produced. Reproducibility was assessed by the adjusted Rand index between the terminal-node partitions of trees refitted on independent imputation draws. Node-level calibration diagnostic A separate study of 20 conditions, reported alongside the ten above and not counted among the 189, isolates the calibration of the Stack/M node-level test. Trees are grown to depth one, so exactly one hypothesis test is performed per replicate and error accumulated across nodes is removed by construction, across missingness rates of 0 to 45% and M = 5 to 50 at n = 1,000, with 2,000 replications per condition. Each replicate is imputed twice from the same data, the same missingness pattern and the same imputation seed, differing only in whether the outcomes enter the predictor matrix. This paired contrast isolates the contribution of outcome-conditioned between-imputation variance and shows that the two imputation models bracket nominal calibration: including the outcome leaves the test anti-conservative, excluding it leaves the test conservative. Contents Table numbers below follow the manuscript, in which Tables 1–10 appear in the main text and Tables S1–S13 in the Supplementary Material. ctreeMI-simulation-code.zip — R scripts implementing the data-generating processes, missingness mechanisms, imputation, fitting and analysis, with the SLURM batch scripts used to run them. The top-level README maps each script to the tables and figures it produces. results-simulation.zip — complete numerical results underlying all tables and figures, each directory holding the raw output in CSV and RDS form with the R session information for the run: results_studies12345/ — Studies 1–5, 282,000 replicate rows, plus 18,000 rows of tree-stability results (Tables 2–6, S1–S9, Figure 1) results_studies67/ — Studies 6–7, 32,400 rows (Table 7, Tables S10–S13, Figure 2) corr_results/ — Studies 8–10, one file per condition, 136,800 rows (Table 9) results_calibration/ — calibration diagnostic under both imputation models, 639,968 rows (Table 8) applied_output/ — brandsma and boys analyses, as text output with plots of the fitted Stack/M trees (Table 10) Reproducibility R 4.6.1 (2026-06-24) on Ubuntu 26.04; ctreeMI 1.0.0, partykit 1.2-29, mice 3.19.0. Each replicate's seed is a deterministic function of its condition and replicate index and is set within the worker process, so results do not depend on the number of processor cores used or on the order in which jobs completed. The Stack/M correction extracts node-level test statistics from partykit internals, so partykit 1.2-29 should be used to reproduce the published results exactly. The applied examples use the brandsma and boys datasets distributed with the mice package. No restricted data are included. Version history Version 2 added the outcome-excluded arm of the calibration diagnostic, so that each replicate is imputed under two imputation models rather than one. The version 1 calibration output is not duplicated in later versions; it remains available in version 1 under its own DOI, and corresponds to the outcome-included arm of the current run, which reproduces it to four decimal places. Version 3 updates the table numbering in both README files to match the final arrangement of the manuscript. No code or results changed. Results for Studies 1–10 and the applied analyses are unchanged from version 1, as is the code that produced them. Related resources ctreeMI on CRAN: https://CRAN.R-project.org/package=ctreeMI Stack/M correction: Sherlock et al. (2026), Multivariate Behavioral Research, doi:10.1080/00273171.2026.2661244

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