Simulating Node Manipulations in Gaussian Graphical Models: The GGMNIRA Framework for Continuous and Ordinal Psychological Network Data

Fei Wang; Hongyun Liu; Yiming Wu

arxiv: 2607.00915 · v1 · pith:GXILLWMBnew · submitted 2026-07-01 · 📊 stat.ME

Simulating Node Manipulations in Gaussian Graphical Models: The GGMNIRA Framework for Continuous and Ordinal Psychological Network Data

Yiming Wu , Fei Wang , Hongyun Liu This is my paper

Pith reviewed 2026-07-02 08:31 UTC · model grok-4.3

classification 📊 stat.ME

keywords Gaussian graphical modelsnode importanceKL divergencepsychological networkssimulation methodsordinal datamoderated models

0 comments

The pith

The GGMNIRA algorithm evaluates node importance in Gaussian graphical models by simulating manipulations to a node's conditional mean and measuring the resulting change in network distribution with KL divergence.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops GGMNIRA to extend simulated node manipulation methods from binary Ising models to Gaussian graphical models suitable for continuous and ordinal psychological data. Centrality measures only describe static positions without clear links to how nodes affect network dynamics. By changing a node's conditional mean and tracking KL divergence shifts, the method aims to identify nodes with greater projected influence on the overall distribution. This provides an alternative to centrality with added tools for stability assessment and bootstrap testing. The approach also handles moderated models for more complex networks.

Core claim

The GGMNIRA framework manipulates a node's conditional mean within the Gaussian graphical model and quantifies the change in the network distribution before and after this manipulation using Kullback-Leibler divergence, thereby extending the logic of simulated node manipulations to continuous and ordinal data and offering a dynamic measure of node importance.

What carries the argument

The GGMNIRA algorithm that manipulates conditional means and applies KL divergence to assess distribution changes in Gaussian graphical models.

If this is right

Node importance can be assessed in psychological networks with continuous or ordinal variables rather than only binary data.
Stability of the KL divergence measures can be evaluated using a new correlation stability coefficient.
Nonparametric bootstrap difference tests allow comparison of KL divergence values between nodes.
The method extends to moderated Gaussian graphical models for analyzing multi-construct networks with interaction effects.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Applying this to real psychological datasets could reveal nodes whose manipulation would most alter symptom networks.
Integration with intervention studies might test whether high-KL nodes correspond to effective treatment targets.
The framework's reliance on conditional mean changes suggests potential for modeling other parameter interventions in future extensions.

Load-bearing premise

That altering a node's conditional mean represents a theoretically meaningful manipulation whose effect on the joint distribution via KL divergence captures influence on network dynamics.

What would settle it

A simulation study in which nodes known to be central by other criteria show no larger KL divergence changes than peripheral nodes after conditional mean manipulation.

read the original abstract

Scientific Abstract: In psychological network analysis, centrality indices are commonly used to evaluate the importance of nodes within a network. However, centrality only captures the static topological position of a node, and there is no sufficient theoretical justification for assuming that it reflects a node's influence on network dynamics. The NodeIdentifyR Algorithm (NIRA) offers an alternative by systematically applying simulated manipulations to node intercepts within the Ising model to evaluate nodes' projected importance, but this algorithm is restricted to binary data, and the manipulated parameter lacks a clear theoretical meaning outside the context of psychopathology. To address these limitations, we propose the Gaussian Graphical Model NodeIdentifyR Algorithm (GGMNIRA), which manipulates a node's conditional mean and uses Kullback-Leibler (KL) divergence to quantify the change in network distribution before and after manipulation, thereby extending this simulated manipulation logic to the Gaussian graphical model framework, which is applicable to continuous and ordinal data. Around this algorithm, we further developed a correlation stability coefficient and a nonparametric bootstrap difference test for KL divergence, with corresponding interpretive thresholds established through simulation studies. The framework was also extended to bridge Gaussian graphical models and moderated Gaussian graphical models, enabling its application to multi-construct comorbidity networks and to contexts involving moderation effects. All methods are implemented in the R package "GGMNIRA".

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

GGMNIRA extends NIRA-style node manipulation to GGMs via conditional-mean shifts and KL divergence, with an R package and stability tools, but the dynamical interpretation of those shifts remains weak.

read the letter

The main takeaway is that this paper takes the NIRA simulation approach from binary Ising models and ports it to Gaussian graphical models. They shift one node's conditional mean, compute the KL divergence between the original and altered joint distributions, and treat the size of that change as a measure of node importance. They also supply an R package, a correlation stability coefficient, a bootstrap difference test, and simulation-based thresholds, plus an extension to moderated GGMs.

What the work actually delivers is concrete and usable. The package implements the procedure for continuous and ordinal data, the stability and bootstrap tools are straightforward to apply, and the moderated extension opens the method to comorbidity-style questions. These pieces are the parts that applied researchers in psychological networks can pick up and run without reinventing the wheel.

The soft spot is the same one flagged in the stress-test note. In a GGM the KL after a mean shift reduces to (1/2) δμ^T Σ^{-1} δμ. That scalar is driven by the node's marginal variance and the global precision matrix; nothing in the construction ties it to an intervention, an edge perturbation, or a change in equilibrium behavior. The paper notes the analogous gap in the binary NIRA but adds no new mapping to psychological mechanisms or dynamics for the continuous case. The simulations check numerical stability, not whether the quantity tracks influence in any external sense.

The math and citation pattern look standard; there is no circularity or invented entities. The work is aimed at the subset of psychological network researchers who already distrust static centrality and want a simulation alternative that works with the data types they actually collect. Readers who need an off-the-shelf R tool for this specific workflow will find it useful.

It deserves peer review. The implementation is real, the extension is well-scoped, and the stability machinery is a practical addition even if the conceptual justification stays thin.

Referee Report

3 major / 2 minor

Summary. The paper introduces the Gaussian Graphical Model NodeIdentifyR Algorithm (GGMNIRA) as an extension of the binary NIRA method. It simulates node manipulations by altering a node's conditional mean in a GGM (or moderated GGM), quantifies the resulting distributional change via KL divergence between the original and manipulated multivariate normals, and supplies a correlation stability coefficient plus nonparametric bootstrap difference test with simulation-derived thresholds. The framework targets continuous/ordinal psychological network data and is implemented in the R package GGMNIRA.

Significance. If the KL-based manipulation procedure can be shown to isolate node influence on network dynamics in a manner not reducible to marginal variance or static centrality, the method would supply a practical tool for comparing node importance in comorbidity and moderated networks. The provision of an R package and simulation-based interpretive thresholds is a concrete implementation strength that would facilitate adoption if the core mapping from mean-shift KL to psychological influence is clarified.

major comments (3)

[Method / Algorithm definition] The central construction manipulates a single component of the conditional mean vector and computes KL(N(μ,Σ), N(μ+δe_i,Σ)) = (1/2)δ² Σ^{-1}_{ii}. This quantity is a direct function of the marginal precision of the manipulated node and does not encode an intervention on edges, a change in equilibrium dynamics, or a causal effect; the same numerical value can arise from shifting an isolated high-variance node or a low-variance hub. The manuscript acknowledges the analogous theoretical gap for binary NIRA but supplies no additional mapping or justification for the continuous/ordinal case that would tie the scalar to 'influence on network dynamics' (see abstract and method description).
[Extension to moderated GGMs] The extension to moderated GGMs is presented as enabling application to multi-construct comorbidity networks, yet the manuscript does not demonstrate that the KL change remains interpretable once moderation parameters alter the precision structure conditionally on another variable. No simulation or analytic result shows that the stability coefficient or bootstrap test controls the relevant error rate under moderation.
[Simulation studies] Simulation studies are used to establish interpretive thresholds for the correlation stability coefficient and bootstrap difference test, but the design does not include a ground-truth recovery experiment in which known node-influence parameters are varied and the KL procedure is evaluated for sensitivity/specificity against those parameters.

minor comments (2)

[Method] Notation for the conditional mean manipulation and the precise definition of the KL divergence (including whether the covariance is held fixed) should be stated explicitly with an equation in the main text.
[Introduction] The abstract states that centrality 'only captures the static topological position' while the new method captures 'influence on network dynamics'; a brief comparison table or figure contrasting the two quantities on the same simulated networks would clarify the claimed distinction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for the constructive and detailed comments on our manuscript. We address each major comment point by point below, with plans for revisions where appropriate to strengthen the work.

read point-by-point responses

Referee: [Method / Algorithm definition] The central construction manipulates a single component of the conditional mean vector and computes KL(N(μ,Σ), N(μ+δe_i,Σ)) = (1/2)δ² Σ^{-1}_{ii}. This quantity is a direct function of the marginal precision of the manipulated node and does not encode an intervention on edges, a change in equilibrium dynamics, or a causal effect; the same numerical value can arise from shifting an isolated high-variance node or a low-variance hub. The manuscript acknowledges the analogous theoretical gap for binary NIRA but supplies no additional mapping or justification for the continuous/ordinal case that would tie the scalar to 'influence on network dynamics' (see abstract and method description).

Authors: We thank the referee for highlighting this key aspect of the construction. The KL divergence does simplify to (1/2)δ² Ω_ii (with Ω = Σ^{-1}), depending on the conditional precision of the node. This is intentional in extending NIRA, as it quantifies the impact of a conditional mean shift on the joint distribution within the fitted GGM, where Ω_ii is shaped by the partial correlation network. While we agree this does not constitute an edge intervention or full causal dynamic (a point already noted for binary NIRA), it offers a distribution-level measure of node manipulation effects that is directly applicable to continuous/ordinal data. To provide the requested additional mapping, we will revise the methods section with an expanded discussion explicitly connecting the KL value to node influence via the network-encoded conditional precision, including examples contrasting hub versus peripheral nodes. revision: yes
Referee: [Extension to moderated GGMs] The extension to moderated GGMs is presented as enabling application to multi-construct comorbidity networks, yet the manuscript does not demonstrate that the KL change remains interpretable once moderation parameters alter the precision structure conditionally on another variable. No simulation or analytic result shows that the stability coefficient or bootstrap test controls the relevant error rate under moderation.

Authors: We agree that explicit validation under moderation is needed to support applications to comorbidity networks. The manuscript derives the moderated extension mathematically but does not include targeted checks. In the revision, we will add simulation studies that vary moderation parameters, assess whether KL divergence remains interpretable as the precision structure becomes conditional, and confirm that the stability coefficient and bootstrap test control error rates appropriately in these settings. revision: yes
Referee: [Simulation studies] Simulation studies are used to establish interpretive thresholds for the correlation stability coefficient and bootstrap difference test, but the design does not include a ground-truth recovery experiment in which known node-influence parameters are varied and the KL procedure is evaluated for sensitivity/specificity against those parameters.

Authors: Our existing simulations establish thresholds for the stability coefficient and bootstrap test under varied network conditions, as described. We recognize the benefit of a ground-truth recovery study for evaluating sensitivity and specificity. We will add such an experiment to the revised manuscript, constructing networks with known differences in node influence (via controlled variations in connection strengths and variances) and assessing the KL-based procedure's ability to recover those differences. revision: yes

Circularity Check

0 steps flagged

No circularity: GGMNIRA is a definitional simulation procedure, not a reduction to fitted inputs or self-citations

full rationale

The paper proposes GGMNIRA by explicitly defining node manipulation via conditional mean shift in the Gaussian graphical model and quantifying impact via KL divergence between pre- and post-manipulation distributions. This is a constructive extension of the NIRA procedure rather than a derivation whose central quantities reduce by construction to the paper's own fitted parameters or prior self-citations. The KL expression is the standard closed-form result for multivariate normals and is applied as a chosen metric, not smuggled in or renamed from an existing result. No load-bearing uniqueness theorem or ansatz from overlapping authors is invoked to force the framework; the method is presented as an independent algorithmic choice with simulation-based thresholds. The acknowledged theoretical gap in interpretation is a validity concern, not a circularity in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The proposal rests on standard assumptions of Gaussian graphical models and KL divergence as a suitable distance; no free parameters or invented entities are described in the abstract.

axioms (1)

domain assumption Gaussian graphical models are appropriate representations for continuous and ordinal psychological network data.
The framework applies directly to GGM without additional justification in the abstract.

pith-pipeline@v0.9.1-grok · 5771 in / 1176 out tokens · 36839 ms · 2026-07-02T08:31:32.442923+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

18 extracted references · 1 canonical work pages

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Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology , 51 (6),

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Barth, J., Munder, T., Gerger, H., Nüesch, E., Trelle, S., Znoj, H., Jüni, P., & Cuijpers, P. (2016). Comparative eﬃcacy of seven psychotherapeutic interventions for patients with depression: A network meta-analysis. Focus, 14 (2), 229–243. Borgatti, S. P. (2005). Centrality and network ﬂow. Social networks , 27 (1), 55–71. Borsboom, D. (2017). A network ...

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Bringmann, L. F., Elmer, T., Epskamp, S., Krause, R. W., Schoch, D., Wichers, M., Wigman, J. T., & Snippe, E. (2019). What do centrality measures measure in psychological networks? Journal of abnormal psychology , 128 (8),

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Burger, J., Isvoranu, A.-M., Lunansky, G., Haslbeck, J., Epskamp, S., Hoekstra, R. H., Fried, E. I., Borsboom, D., & Blanken, T. F. (2023). Reporting standards for psychological network analyses in cross-sectional data. Psychological methods, 28 (4),

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Carter, J. S., Rossell, D., & Smith, J. Q. (2024). Partial correlation graphical lasso. Scandinavian Journal of Statistics , 51 (1), 32–63. Castro, D., Ferreira, F., de Castro, I., Rodrigues, A. R., Correia, M., Ribeiro, J., & Ferreira, T. B. (2019). The diﬀerential role of central and bridge symptoms in deactivating psychopathological networks. Frontiers...

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Dalege, J., Borsboom, D., Van Harreveld, F., Van den Berg, H., Conner, M., & Van der Maas, H. L. (2016). Toward a formalized account of attitudes: The causal attitude network (can) model. Psychological review, 123 (1),

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Efron, B. (1992). Bootstrap methods: Another look at the jackknife. In Breakthroughs in statistics: Methodology and distribution (pp. 569–593). Springer. Epskamp, S., Borsboom, D., & Fried, E. I. (2018). Estimating psychological networks and their accuracy: A tutorial paper. Behavior research methods, 50 (1), 195–212. Epskamp, S., & Fried, E. I. (2018). A...

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Epskamp, S., Waldorp, L. J., Mõttus, R., & Borsboom, D. (2018). The gaussian graphical model in cross-sectional and time-series data. Multivariate behavioral research, 53 (4), 453–480. Eronen, M. I. (2020). Causal discovery and the problem of psychological interventions. New Ideas in Psychology , 59, 100785. Fisher, R. A. (1921). On the" probable error" o...

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GGMNIRA: SIMULATING NODE MANIPULATIONS 60 Guest, O., & Martin, A. E. (2021). How computational modeling can force theory building in psychological science. Perspectives on Psychological Science , 16 (4), 789–802. Hallquist, M. N., Wright, A. G., & Molenaar, P. C. (2021). Problems with centrality measures in psychopathology symptom networks: Why network ps...

2021
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A., Wichern, D

Johnson, R. A., Wichern, D. W., et al. (2002). Applied multivariate statistical analysis. Jones, P. J., Ma, R., & McNally, R. J. (2021). Bridge centrality: A network approach to understanding comorbidity. Multivariate behavioral research, 56 (2), 353–367. Kullback, S. (1951). Kullback-leibler divergence. Tech. Rep. Lauritzen, S. L. (1996). Graphical model...

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Sala, M., Aslan, M., Gueorguieva, R., Schupak, M., & Garrison, K. A. (2023). A network investigation of core mindfulness processes. Mindfulness, 14 (4), 992–1004. GGMNIRA: SIMULATING NODE MANIPULATIONS 62 Sekulovski, N., Blanken, T. F., Haslbeck, J. M., & Marsman, M. (2025). The impact of dichotomization on network recovery. Behavior Research Methods, 57 (12),

2023
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Shang, Z., & Sun, X. (2025). Understanding depressive symptomatology and the associated factors among chinese adolescents: A network approach. Child Psychiatry & Human Development, 1–21. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology , 58 (1), 267–288. Van...

2025
[14]

Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C. (2021). Rank-normalization, folding, and localization: An improved rhat for assessing convergence of mcmc (with discussion). Bayesian Analysis, 16 (2), 667–718. https://doi.org/10.1214/20-BA1221 Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems of p values. Psych...

work page doi:10.1214/20-ba1221 2021
[15]

J., & Strogatz, S

GGMNIRA: SIMULATING NODE MANIPULATIONS 63 Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of small-worldnetworks. nature, 393 (6684), 440–442. Wu, Y., Zhou, W., Liu, F., Meng, X., & Wang, F. (2026). Daily dynamics of rest intolerance, anxiety, and problematic smartphone use: Insights from 14-day intensive longitudinal study. Personality and In...

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[16]

segregated

Although strength centrality and GGMNIRA identiﬁed diﬀerent nodes as the most important node, such a high correlation makes it necessary to further understand the fundamental relationship between the two. This subsection aims to answer three key questions: whether GGMNIRA diﬀers from strength centrality, why it diﬀers, and under what conditions it diﬀers....

1996
[17]

That is, one GGMNIRA: SIMULATING NODE MANIPULATIONS 71 variable was randomly selected from each of the two dimensions, and a weak edge was generated between them

In addition, to avoid the possibility that no edge would appear between dimensions under the low between-dimension density condition, we added one rule across all conditions. That is, one GGMNIRA: SIMULATING NODE MANIPULATIONS 71 variable was randomly selected from each of the two dimensions, and a weak edge was generated between them. This procedure ensu...

2026
[18]

We then compared the correlation between the GGMNIRA results and the strength centrality results under the 81 conditions to support our reasoning

in the manuscript, we further obtained the partial correlation matrix and the regression coeﬃcient matrix. We then compared the correlation between the GGMNIRA results and the strength centrality results under the 81 conditions to support our reasoning. To enhance the robustness of this simulation study, we generated 1,000 networks under each condition us...

1921

[1] [1]

M., & Kenny, D

Baron, R. M., & Kenny, D. A. (1986). The moderator–mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of personality and social psychology , 51 (6),

1986

[2] [2]

Barth, J., Munder, T., Gerger, H., Nüesch, E., Trelle, S., Znoj, H., Jüni, P., & Cuijpers, P. (2016). Comparative eﬃcacy of seven psychotherapeutic interventions for patients with depression: A network meta-analysis. Focus, 14 (2), 229–243. Borgatti, S. P. (2005). Centrality and network ﬂow. Social networks , 27 (1), 55–71. Borsboom, D. (2017). A network ...

2016

[3] [3]

F., Elmer, T., Epskamp, S., Krause, R

Bringmann, L. F., Elmer, T., Epskamp, S., Krause, R. W., Schoch, D., Wichers, M., Wigman, J. T., & Snippe, E. (2019). What do centrality measures measure in psychological networks? Journal of abnormal psychology , 128 (8),

2019

[4] [4]

H., Fried, E

Burger, J., Isvoranu, A.-M., Lunansky, G., Haslbeck, J., Epskamp, S., Hoekstra, R. H., Fried, E. I., Borsboom, D., & Blanken, T. F. (2023). Reporting standards for psychological network analyses in cross-sectional data. Psychological methods, 28 (4),

2023

[5] [5]

S., Rossell, D., & Smith, J

Carter, J. S., Rossell, D., & Smith, J. Q. (2024). Partial correlation graphical lasso. Scandinavian Journal of Statistics , 51 (1), 32–63. Castro, D., Ferreira, F., de Castro, I., Rodrigues, A. R., Correia, M., Ribeiro, J., & Ferreira, T. B. (2019). The diﬀerential role of central and bridge symptoms in deactivating psychopathological networks. Frontiers...

2024

[6] [6]

GGMNIRA: SIMULATING NODE MANIPULATIONS 59 Cohen, J. (2013). Statistical power analysis for the behavioral sciences . routledge. Cramer, A. O., Van der Sluis, S., Noordhof, A., Wichers, M., Geschwind, N., Aggen, S. H., Kendler, K. S., & Borsboom, D. (2012). Dimensions of normal personality as networks in search of equilibrium: You can’t like parties if you...

2013

[7] [7]

Dalege, J., Borsboom, D., Van Harreveld, F., Van den Berg, H., Conner, M., & Van der Maas, H. L. (2016). Toward a formalized account of attitudes: The causal attitude network (can) model. Psychological review, 123 (1),

2016

[8] [8]

Efron, B. (1992). Bootstrap methods: Another look at the jackknife. In Breakthroughs in statistics: Methodology and distribution (pp. 569–593). Springer. Epskamp, S., Borsboom, D., & Fried, E. I. (2018). Estimating psychological networks and their accuracy: A tutorial paper. Behavior research methods, 50 (1), 195–212. Epskamp, S., & Fried, E. I. (2018). A...

1992

[9] [9]

probable error

Epskamp, S., Waldorp, L. J., Mõttus, R., & Borsboom, D. (2018). The gaussian graphical model in cross-sectional and time-series data. Multivariate behavioral research, 53 (4), 453–480. Eronen, M. I. (2020). Causal discovery and the problem of psychological interventions. New Ideas in Psychology , 59, 100785. Fisher, R. A. (1921). On the" probable error" o...

2018

[10] [10]

GGMNIRA: SIMULATING NODE MANIPULATIONS 60 Guest, O., & Martin, A. E. (2021). How computational modeling can force theory building in psychological science. Perspectives on Psychological Science , 16 (4), 789–802. Hallquist, M. N., Wright, A. G., & Molenaar, P. C. (2021). Problems with centrality measures in psychopathology symptom networks: Why network ps...

2021

[11] [11]

A., Wichern, D

Johnson, R. A., Wichern, D. W., et al. (2002). Applied multivariate statistical analysis. Jones, P. J., Ma, R., & McNally, R. J. (2021). Bridge centrality: A network approach to understanding comorbidity. Multivariate behavioral research, 56 (2), 353–367. Kullback, S. (1951). Kullback-leibler divergence. Tech. Rep. Lauritzen, S. L. (1996). Graphical model...

2002

[12] [12]

Sala, M., Aslan, M., Gueorguieva, R., Schupak, M., & Garrison, K. A. (2023). A network investigation of core mindfulness processes. Mindfulness, 14 (4), 992–1004. GGMNIRA: SIMULATING NODE MANIPULATIONS 62 Sekulovski, N., Blanken, T. F., Haslbeck, J. M., & Marsman, M. (2025). The impact of dichotomization on network recovery. Behavior Research Methods, 57 (12),

2023

[13] [13]

Shang, Z., & Sun, X. (2025). Understanding depressive symptomatology and the associated factors among chinese adolescents: A network approach. Child Psychiatry & Human Development, 1–21. Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society Series B: Statistical Methodology , 58 (1), 267–288. Van...

2025

[14] [14]

Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P.-C. (2021). Rank-normalization, folding, and localization: An improved rhat for assessing convergence of mcmc (with discussion). Bayesian Analysis, 16 (2), 667–718. https://doi.org/10.1214/20-BA1221 Wagenmakers, E.-J. (2007). A practical solution to the pervasive problems of p values. Psych...

work page doi:10.1214/20-ba1221 2021

[15] [15]

J., & Strogatz, S

GGMNIRA: SIMULATING NODE MANIPULATIONS 63 Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of small-worldnetworks. nature, 393 (6684), 440–442. Wu, Y., Zhou, W., Liu, F., Meng, X., & Wang, F. (2026). Daily dynamics of rest intolerance, anxiety, and problematic smartphone use: Insights from 14-day intensive longitudinal study. Personality and In...

1998

[16] [16]

segregated

Although strength centrality and GGMNIRA identiﬁed diﬀerent nodes as the most important node, such a high correlation makes it necessary to further understand the fundamental relationship between the two. This subsection aims to answer three key questions: whether GGMNIRA diﬀers from strength centrality, why it diﬀers, and under what conditions it diﬀers....

1996

[17] [17]

That is, one GGMNIRA: SIMULATING NODE MANIPULATIONS 71 variable was randomly selected from each of the two dimensions, and a weak edge was generated between them

In addition, to avoid the possibility that no edge would appear between dimensions under the low between-dimension density condition, we added one rule across all conditions. That is, one GGMNIRA: SIMULATING NODE MANIPULATIONS 71 variable was randomly selected from each of the two dimensions, and a weak edge was generated between them. This procedure ensu...

2026

[18] [18]

We then compared the correlation between the GGMNIRA results and the strength centrality results under the 81 conditions to support our reasoning

in the manuscript, we further obtained the partial correlation matrix and the regression coeﬃcient matrix. We then compared the correlation between the GGMNIRA results and the strength centrality results under the 81 conditions to support our reasoning. To enhance the robustness of this simulation study, we generated 1,000 networks under each condition us...

1921