Hierarchical Validation of Candidate Hyperedges

Performs hierarchical validation to determine whether a significant higher-order interaction provides information beyond its lower-order subsets.

Usage

hierarchical_validation(results_df, subset_results = NULL)

Arguments

results_df

Data frame produced during the significance-testing pipeline.

subset_results

Optional data frame of comparison intervals with columns vars, boot_ci_lower, and boot_ci_upper. Supplied intervals take precedence over matching rows in results_df.

Value

The input data frame with an additional logical column:

hierarchical_valid

Whether the hyperedge survives hierarchical validation.

Details

This procedure corresponds to the third stage of hypergraph construction framework proposed by Marinazzo et al. (2024) and adopted by Possenti et al. (2026).

For each robust k-order multiplet, the BCa confidence interval of its O-information is compared against the confidence intervals of all nested (k-1)-order subsets.

If the confidence interval overlaps with any nested subset, the higher-order interaction is considered non-informative because its effect may be explained by lower-order dependencies.

Hyperedges that do not overlap with any nested subset are considered hierarchically valid.

The rationale is that genuine higher-order interactions should contribute information that cannot be fully attributed to any lower-order component.

Robust third-order multiplets with valid intervals are considered hierarchically valid without a lower-order comparison. For higher orders, missing or invalid subset intervals prevent validation. Any interval intersection, including contact at an endpoint, counts as overlap. Only immediate (k-1)-order subsets are compared.

References

Marinazzo, D., Van Roozendaal, J., Rosas, F. E., Stella, M., Comolatti, R., Colenbier, N., Stramaglia, S., & Rosseel, Y. (2024). An information-theoretic approach to build hypergraphs in psychometrics. Behavior Research Methods, 56(7), 8057-8079.

Possenti, F., Girelli, L., Tieri, P., & Petti, M. (2026). Multiplex Hypergraph Modeling of Higher Order Structures in Psychometric Networks (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2604.22744