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The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction.

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  1. [1] § STAR★Methods › Quantification and statistical analysis › Prewhitening ↔ fit_models.m, lines 34–120 · score 0.55 · regression coefficients, node pairs, residuals, ij, matrix

Paper

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The authors' code

MATLAB · 120 lines · 3.4 KB · no license · 1 match

  1. clear all
  2. close all
  3. clc
  5. %% Description
  6. %
  7. % In this script, we read in time series data -- parcel-level Ca++
  8. % imaging data and behavioral time courses. The goals is to fit lineaer
  9. % models that explain the behavioral data in terms of:
  10. %
  11. % 1. the z-scored activity of parcel i,
  12. % 2. the z-scored activity of parcel j,
  13. % 3. the element-wise product of those z-scored time series (referred
  14. % to in our previous work as an 'edge time series').
  15. %
  16. % This procedure is repeated for all unique {i,j} pairs, populating
  17. % matrices of regression coefficients.
  18. %
  19. % We repeat this entire procedure for seven behavioral time courses. For
  20. % reference, these data come from 'subject 18' in this paper:
  21. %
  22. % Chen, X., Mu, Y., Hu, Y., Kuan, A. T., Nikitchenko, M.,
  23. % Randlett, O., ... & Ahrens, M. B. (2018). Brain-wide organization
  24. % of neuronal activity and convergent sensorimotor transformations in
  25. % larval zebrafish. Neuron, 100(4), 876-890.
  26. %
  27. % If you use this code in your own work, please cite the original data
  28. % source, but also our paper:
  29. %
  30. % Merritt, H., Mejia, A., & Betzel, R. (2024). The dual
  31. % interpretation of edge time series: Time-varying connectivity
  32. % versus statistical interaction. bioRxiv, 2024-08.
  34. %% Analysis
  36. % load data
  37. load data
  39. z = zscore(z); % z-score time series
  41. [nt,n] = size(z); % number of frames, number of parcels
  42. [u,v] = find(triu(ones(n),1)); % upper triangle indices
  44. % outer loop - over behavioral measures
  45. for j = 1:size(b,2)
  47. % behavior time series
  48. y = b(:,j);
  50. % constants
  51. nobs = length(y);
  52. dft = nobs - 1;
  53. dfe = nobs - 4;
  54. p = 4;
  56. % more constants
  57. ybar = mean(y);
  58. sst = norm(y - ybar)^2;
  60. % preallocate arrays for rsquared, regression coefficients, and pvalues
  61. rsqu = zeros(length(u),1);
  62. betas = zeros(length(u),p);
  63. pvals = zeros(length(u),p);
  65. % loop over all node pairs
  66. for i = 1:length(u)
  68. % update
  69. if mod(i,round(length(u)/51)) == 0
  70. fprintf('behavioral measure %i, %.2f percent complete (%i of %i edges)\n',j,100*i/length(u),i,length(u));
  71. end
  73. % matrix of explanatory values
  74. x = ones(nt,4);
  75. x(:,1) = z(:,u(i));
  76. x(:,2) = z(:,v(i));
  77. x(:,3) = z(:,u(i)).*z(:,v(i));
  79. % get betas and pvalues
  80. [Q,R] = qr(x,0);
  82. % regression coefficients -- could stop here if we didn't want to
  83. % do states
  84. beta = R\(Q'*y);
  86. % behavior predicted by model + residuals
  87. yhat = x*beta;
  88. residuals = y - yhat;
  90. sse = norm(residuals)^2;
  91. mse = sse./dfe;
  92. ri = R\eye(p);
  93. xtxi = ri*ri';
  94. covb = xtxi*mse;
  95. se = sqrt(diag(covb));
  97. % t-statistic, pvalue (from distribution)
  98. t = beta./se;
  99. pval = 2*(tcdf(-abs(t),dfe));
  101. % keep rsquared, betas, and pvalues
  102. rsqu(i) = 1 - sse./sst;
  103. betas(i,:) = beta;
  104. pvals(i,:) = pval;
  106. end
  108. % plot the three matrices -- here, we only show upper triangle
  109. s = zeros(1,3);
  110. tnames = {'beta_i','beta_j','beta_{ij}'};
  111. figure;
  112. for i = 1:3
  113. m = zeros(n);
  114. m(triu(ones(n),1) > 0) = betas(:,i);
  115. s(i) = subplot(1,3,i); imagesc(m); title(tnames{i}); xlabel('parcels'); ylabel('parcels');
  116. end
  117. set(s,'clim',[-max(abs(m(:))),max(abs(m(:)))]*0.25);
  118. drawnow;
  120. end

fit_models.m at commit f9f6238, no license · at the source

Overview

Authors: Haily Merritt1,2, Amanda Mejia3, Richard Betzel1,4,5,6
ORCID iDs: Richard Betzel
  1. Cognitive Science Program, Indiana University, Bloomington, IN, USA
  2. School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA
  3. Department of Statistics, Indiana University, Bloomington, IN, USA
  4. Department of Neuroscience, University of Minnesota, Minneapolis, MN, USA
  5. Masonic Institute for the Developing Brain, University of Minnesota, Minneapolis, MN, USA
  6. Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA
Institutions: Indiana University Bloomington (United States); Indiana University (United States); University of Minnesota (United States)
Journal: iScience, volume 29, issue 6, article 115949
Dates: received 19 September 2024; accepted 27 April 2026; published online 22 May 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1016/j.isci.2026.115949 · PMID 42231974 · PMCID PMC13224015 · OpenAlex W4402098305
Open access: gold, a free copy (OpenAlex)
Preprint: doi:10.1101/2024.08.29.609259
Status: code verified
Methods: Spectral & time-frequency, Statistics, Preprocessing, Graphs, Single-unit activity, calcium imaging, Smoothing, state filtering, decompositions
Keywords: natural sciences, biological sciences, neuroscience, systems neuroscience, techniques in neuroscience
Topic: Complex Systems and Time Series Analysis (Economics and Econometrics, Economics, Econometrics and Finance), according to OpenAlex
Funding: Neighborhood Coalition for Shelter; National Science Foundation; National Institute on Aging; National Science Foundation Division of Information and Intelligent Systems (2023985)
Citations: cited by 1 paper (Europe PMC); 96 references in the paper
Research resources: NiLearn RRID:SCR_001362http, MATLAB RRID:SCR_001622https, Freesurfer RRID:SCR_001847https, Brain Connectivity Toolbox RRID:SCR_004841https, fMRIPrep RRID:SCR_016216https

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repositories

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Zenodo 18377915

License: MIT
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data and code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (3 files)
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
  • 28 September 2026: the link answers (HTTP 200)
8 files
At the source: doi.org/10.5281/zenodo.18377915

Zenodo 18377883

License: CC-BY-4.0
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data and code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
  • 28 September 2026: the link answers (HTTP 200)
2 files
At the source: doi.org/10.5281/zenodo.18377883

brain-networks/ets_glms

License: none: the authors keep all their rights
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: f9f6238da55c6121880a412c901db56888a95f2b, 14 November 2025
Languages: MATLAB (1)
Size: 3 files, 1 script
Software Heritage: not archived
Found in: the Zenodo archive record
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
2 files
At the source: github.com/brain-networks/ets_glms/tree/v0.1

brain-networks/edge-centric_demo

License: MIT
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: 87f1b65890274f63b97dc62e647bd730321d58a9, 6 November 2020
Languages: MATLAB (6)
Size: 12 files, 6 scripts
Software Heritage: archived
Found in: the Zenodo archive record
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (3 files)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
8 files
At the source: github.com/brain-networks/edge-centric_demo/tree/v0.1

The paper's code and data availability statement is in the Data section.

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Data

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Read them in the paper: doi.org/10.1016/j.isci.2026.115949.

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Version 2, 28 September 2026

  • Authors: added Richard Betzel (0000-0001-9200-1681); removed Richard Betzel

Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 4 funders, 89 references, 5 RRIDs.

Cite

This paper

Merritt, H., Mejia, A., & Betzel, R. (2026). The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction. iScience, 29(6), 115949. https://doi.org/10.1016/j.isci.2026.115949

BibTeX

@article{merritt2026dual,
author = {Merritt, Haily and Mejia, Amanda and Betzel, Richard},
title = {{The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction}},
journal = {iScience},
year = {2026},
month = may,
volume = {29},
number = {6},
pages = {115949},
publisher = {Elsevier},
issn = {2589-0042},
doi = {10.1016/j.isci.2026.115949},
url = {https://doi.org/10.1016/j.isci.2026.115949},
pmid = {42231974},
pmcid = {PMC13224015}
}

RIS

TY - JOUR
AU - Merritt, Haily
AU - Mejia, Amanda
AU - Betzel, Richard
TI - The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction
T2 - iScience
J2 - iScience
PY - 2026
DA - 2026/05/22
VL - 29
IS - 6
SP - 115949
SN - 2589-0042
PB - Elsevier
DO - 10.1016/j.isci.2026.115949
UR - https://doi.org/10.1016/j.isci.2026.115949
LA - en
ER -

CSL-JSON

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