int3ract: Johnson-Neyman Technique and its Three-Way Extension for Frequentist and Bayesian Models in R
Pith reviewed 2026-05-09 20:36 UTC · model grok-4.3
The pith
The int3ract R package implements the Johnson-Neyman technique for two-way interactions and its three-way extension for frequentist and Bayesian models.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The int3ract package provides the JNK_freq function for frequentist models and JNK_bayes for Bayesian models to compute and plot regions of significance for two- and three-way interactions, replacing the spotlight approach with region-specific analysis.
What carries the argument
The Johnson-Neyman-Krause technique, an extension of the Johnson-Neyman method that solves for the values of moderators where the conditional effect's confidence interval or posterior excludes zero.
Load-bearing premise
The fitted statistical model is correctly specified and its coefficient estimates and covariance matrix accurately represent the data-generating process.
What would settle it
Running the JNK technique on a simulated dataset with a known three-way interaction structure and checking whether the computed significant regions match the true ranges where the effect is non-zero.
Figures
read the original abstract
Interaction effects are ubiquitous in applied statistical modelling, yet their meaningful interpretation remains challenging. The classic Johnson-Neyman (JN) technique (Johnson and Neyman 1936) addresses this challenge for two-way interactions by identifying the regions of a moderator's range over which a focal effect is and is not statistically significant. The int3ract package for R implements the JN technique and its three-way extension (the Johnson-Neyman-Krause, or JNK, technique) for both frequentist and Bayesian models. The function JNK_freq() auto-detects models fitted via lm()/glm(), RSiena's siena(), or lme4's lmer()/glmer(), but can also be applied to multiplicative interactions from (virtually) any model family by supplying a coefficient vector and covariance matrix directly. For Bayesian Stochastic Actor-Oriented Models (SAOMs) estimated with multiSiena, or any model producing posterior draws, the function JNK_bayes() produces conditional posterior distributions. For two-way interactions, classic shaded confidence-band plots are created that visually demarcate significant and non-significant regions along the moderator range; three-way interactions yield colour-gradient heatmaps with optional crosshatch overlays for non-significant regions. The package is designed to encourage richer, region-specific reporting of interaction effects in place of the conventional single-slope spotlight approach.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript describes the int3ract R package, which implements the classic Johnson-Neyman (JN) technique for two-way interactions and its three-way extension (Johnson-Neyman-Krause or JNK technique) for both frequentist and Bayesian models. The JNK_freq() function auto-detects fitted models from lm/glm, RSiena's siena, or lme4's lmer/glmer (with direct coefficient and covariance matrix input supported for other families), while JNK_bayes() handles posterior draws; visualization includes shaded confidence-band plots for two-way cases and color-gradient heatmaps with optional crosshatch overlays for three-way cases.
Significance. If the implementation is correct, the package would provide a practical tool for applied researchers to report region-specific significance of interaction effects rather than relying on the spotlight approach, supporting richer interpretation in fields using linear, generalized linear, multilevel, and stochastic actor-oriented models. It fills a gap in accessible software for the JNK extension and Bayesian handling, with potential to improve reporting standards for interactions.
major comments (2)
- [Description of JNK_freq() and auto-detection logic] The central claim that JNK_freq() correctly implements the JN and JNK procedures (including auto-detection for the listed model classes) is not supported by any verification against known analytic results or test cases for standard models (e.g., a linear regression with a two-way interaction term). Without such checks, the accuracy of the derived regions of significance cannot be confirmed.
- [Bayesian implementation section] For the Bayesian case in JNK_bayes(), the manuscript describes production of conditional posterior distributions but provides no details on error propagation, credible interval construction, or handling of posterior uncertainty in the three-way JNK extension; this is load-bearing for users relying on the function with models producing posterior draws.
minor comments (2)
- [Direct coefficient input description] The claim of support for 'virtually any model family' via direct coefficient input would benefit from explicit discussion of assumptions or limitations (e.g., regarding the form of the interaction term or covariance structure).
- [Visualization options] Inclusion of example code snippets or output figures demonstrating the plots (shaded bands and heatmaps) would improve clarity and usability for readers.
Simulated Author's Rebuttal
We thank the referee for their constructive comments and positive assessment of the int3ract package. We address each major comment below and will revise the manuscript accordingly to strengthen the presentation of the implementation.
read point-by-point responses
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Referee: The central claim that JNK_freq() correctly implements the JN and JNK procedures (including auto-detection for the listed model classes) is not supported by any verification against known analytic results or test cases for standard models (e.g., a linear regression with a two-way interaction term). Without such checks, the accuracy of the derived regions of significance cannot be confirmed.
Authors: We agree that explicit verification would improve the manuscript. In the revised version we will add a validation subsection that applies JNK_freq() to a standard linear regression with a two-way interaction term, compares the resulting regions of significance against analytically derived values, and provides analogous checks for the three-way JNK extension on supported model classes (lm, lmer, siena). Direct coefficient-and-covariance input will also be verified against the same analytic benchmarks. revision: yes
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Referee: For the Bayesian case in JNK_bayes(), the manuscript describes production of conditional posterior distributions but provides no details on error propagation, credible interval construction, or handling of posterior uncertainty in the three-way JNK extension; this is load-bearing for users relying on the function with models producing posterior draws.
Authors: We acknowledge that the current text is insufficiently detailed on these points. We will expand the Bayesian implementation section to describe (i) how posterior draws are used to form conditional posterior distributions of the focal effect, (ii) propagation of uncertainty through the linear predictor and variance terms, (iii) credible-interval construction via quantiles of the conditional posteriors, and (iv) the specific adaptations required for the three-way JNK extension. These additions will make the procedure fully transparent to users. revision: yes
Circularity Check
No significant circularity; software implementation of established JN technique
full rationale
The manuscript is a package description documenting the int3ract R package's implementation of the classic Johnson-Neyman (1936) technique and its three-way extension for frequentist and Bayesian models. No derivation chain, predictions, or first-principles results are asserted that could reduce to inputs by construction. The paper presents no self-referential equations, fitted parameters renamed as predictions, or load-bearing self-citations that justify a novel claim. References to the JNK extension and model auto-detection are descriptive of the software's functionality rather than circular statistical arguments. The central content is implementation details for lm/glm, siena, lmer/glmer, and direct coefficient input, which are independent of any circular reduction.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption The fitted model is correctly specified and the coefficient vector plus covariance matrix fully capture the sampling distribution of the interaction terms.
Reference graph
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discussion (0)
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