rescale_statistic: Rescale a Node-Level Test Statistic for Stacking

In ctreeMI: Conditional Inference Trees with Stacked Multiple Imputation

Rescale a Node-Level Test Statistic for Stacking

Description

Divides a node-level chi-square test statistic by the number of imputations M and recomputes the corresponding p-value. This is the Stack / M correction of Sherlock et al. (2026).

Usage

rescale_statistic(statistic, m, df)

Arguments

statistic	Numeric. The raw test statistic computed on the stacked data.
m	Integer. Number of imputations.
df	Numeric. Degrees of freedom of the reference chi-square distribution: the outcome dimension for a numeric or ordered predictor, (L - 1) times the outcome dimension for an unordered factor with L levels. See prune_stackM(), which derives this for you.

Details

Stacking M imputed datasets produces M * n rows, and a chi-square statistic computed on the stacked data scales approximately linearly with M. Dividing the statistic by M returns it to the scale of a single imputed dataset before the p-value is computed.

This is not the same as dividing the significance threshold by M. The two rules coincide only at M = 1:

• Statistic rescaling rejects when X > M * qchisq(1 - alpha, df).

• Threshold rescaling rejects when X > qchisq(1 - alpha / M, df).

For df = 1, alpha = 0.05 and M = 30, the first requires X > 115.2 and the second only X > 9.9. Versions 0.1.0 and 0.2.0 implemented the second rule.

Value

A list with statistic_rescaled and p_value.

References

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00273171.2026.2661244")}

Examples

rescale_statistic(115.2, m = 30, df = 1)

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