Testing for interactions in multivariate data.

Code ↔ Paper

12 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 12 matches · all tie a paragraph to a whole file without given lines: weak matches, whose lines are not tinted

[1] § Materials and methods › Decoding methods ↔ misc/svm_classify.m, the whole file · a weak match · score 0.68 · Nearest Neighbour, fitcecoc, fitcknn, fitclinear, fitcsvm, classifier · Report a mismatch
[2] § Materials and methods › Decoding methods ↔ misc/svm_classify_old.m, the whole file · a weak match · score 0.68 · Nearest Neighbour, fitcecoc, fitcknn, fitclinear, fitcsvm, classifier · Report a mismatch
[3] § Materials and methods › Reward learning ↔ data/get_reward_data.m, the whole file · a weak match · score 0.66 · median split, RPE sign, trajectories, grand, Reward · Report a mismatch
[4] § Materials and methods › Multivariate linear model with conjugate priors › Likelihood. ↔ linear-regression/bayes_glinear_estimate.m, the whole file · a weak match · score 0.64 · regression coefficients, independent variables, noise, Gaussian, covariance, zero · Report a mismatch
[5] § Materials and methods › Multivariate linear model with conjugate priors › Likelihood. ↔ linear-regression/bayes_glm_regression.m, the whole file · a weak match · score 0.64 · multivariate Gaussian, independent variables, regression, noise, coefficients, errors · Report a mismatch
[6] § Materials and methods › Univariate methods ↔ toolbox/plot_anova_map.m, the whole file · a weak match · score 0.62 · Benjamini Hochberg, FDR correction, BH, map, hypotheses · Report a mismatch
[7] § Materials and methods › Multivariate linear model with conjugate priors › Factorial designs. ↔ linear-regression/bayes_glm_anova1.m, the whole file · a weak match · score 0.60 · way ANOVAs, log Bayes factor, alternative hypothesis, favour, model · Report a mismatch
[8] § Materials and methods › Univariate methods ↔ toolbox/plot_classifier_results.m, the whole file · a weak match · score 0.58 · Benjamini Hochberg, FDR correction, BH · Report a mismatch
[9] § Materials and methods › Multivariate linear model with conjugate priors › Factorial designs. ↔ misc/savage_dickey_vector.m, the whole file · a weak match · score 0.58 · Savage Dickey, contrast matrix, posterior · Report a mismatch
[10] § Materials and methods › Multivariate linear model with conjugate priors › Factorial designs. ↔ linear-regression/bayes_glm_regression.m, the whole file · a weak match · score 0.55 · Savage Dickey, design matrix, fitting, posterior, Bayesian, model · Report a mismatch
[11] § Materials and methods › Multivariate linear model with conjugate priors › Bayes factors. ↔ misc/savage_dickey_vector.m, the whole file · a weak match · score 0.51 · log Bayes Factor, alternative hypothesis, enforce, probability, posterior · Report a mismatch
[12] § Materials and methods › Decoding methods ↔ toolbox/plot_classifier_results.m, the whole file · a weak match · score 0.51 · Benjamini Hochberg procedure, classification, FDR · Report a mismatch

Paper

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The authors' code

MATLAB · 106 lines · 2.9 KB · no license · 2 matches

function [logBF,glm] = bayes_glm_regression (X,y,method)
% Bayesian GLM regression
% FORMAT [logBF,glm] = bayes_glm_regression (X,y,method)
%
% X [N x K] Design matrix (Independent Variables).
% Kth column must be vector of 1's.
% y [N x 1] Dependent Variable
% method 'G' Multivariate Gaussian priors and posteriors
% 'T' Multivariate T (MVT) priors and posteriors
%
% Log Bayes Factors in favour of alternative hypothesis:
% logBF(1) Fit Full and Reduced Model separately (Multi-Fitting)
% logBF(2) Savage-Dickey
% logBF(3) Default Bayes Factors
%
% glm Linear Model parameters
%
% Single variance component assumed
[N,K] = size(X);
% Check Kth column is vector of 1's
d=X(:,K)-ones(N,1);
if sum(d.^2) > 0
disp('Error in bayes_glm_regression: last column of design matrix must be column of 1''s.');
return
end
% Centre design matrix - as in Rouder and Morey (2013)
for p=1:K-1,
X(:,p)=X(:,p)-mean(X(:,p));
end
% Subtract data mean
my = mean(y);
vy = std(y)^2;
y = y-my;
% Prior precision/variance matrices
XK = X(:,1:K-1);
B0 = (XK'*XK)/N;
B0 = blkdiag(B0,1);
% Rouder and Morey (2013) set the prior covariance of regression
% coefficients to be proportional to inv(B0). Hence choice of the
% above term.
switch method
case 'T',
% Single variance component assumed - intrinsic to MVT prior
% c0 must be larger than 1 for finite variance
% 2*c0 is the degrees of freedom of T-prior
% (c0=1/2 for Cauchy)
glm.c0=1.1;
glm.B0=B0;
glm.w0=zeros(K,1);
% Scale observation noise level to variance of dependent variable.
% This then changes scale of prior variance over regression
% coefficients through T-prior.
glm.b0 = 1/(glm.c0*vy);
% Define null model
glm_null = glm;
glm_null.w0 = glm.w0(K);
glm_null.B0 = glm.B0(K,K);
case 'G',
glm.pE=zeros(K,1);
% Single variance component assumed
glm.Ce=vy*eye(N); % IID Error matrix
% Scale prior variance by data variability
C0 = inv(B0);
glm.pC=vy*C0;
% Define null model
glm_null = glm;
glm_null.pE = glm.pE(K);
glm_null.pC = glm.pC(K,K);
otherwise
disp('Unknown method in bayes_glm_regression.m');
return
end
glm.X = X;
glm_null.X = glm.X(:,K);
glm = bayes_linear_estimate (glm,y,method);
% Savage-Dickey
c = eye(K);
logBF(2) = bayes_linear_test (glm,c,method);
% Fit null model
glm_null = bayes_linear_estimate (glm_null,y,method);
logBF(1) = glm.F - glm_null.F;
% Default Bayes Factor
R2 = glm.R2;
bf10 = linregbf(R2,N,K-1);
logBF(3) = log(bf10);

bayes_glm_regression.m at commit 60e6aff, no license · at the source

Overview

Authors: Will Penny¹, Tom Sambrook¹, Louis Renoult¹

ORCID iDs: Will Penny, Louis Renoult

School of Psychology, University of East Anglia, Norwich, United Kingdom

Institutions: University of East Anglia (United Kingdom)

Journal: PloS one, volume 21, issue 11, article e0338580

Dates: received 19 December 2025; accepted 29 September 2026; published online 10 November 2026

Type: Research article · Language: English

License: CC BY

Identifiers: DOI 10.1371/journal.pone.0338580 · PMID 43008059 · PMCID PMC13750587 · OpenAlex W4416889594

Open access: gold, a free copy (OpenAlex)

Preprint: doi:10.1101/2025.11.26.690868

Status: code verified (how the code is found and verified)

Categories: EEG (modality), human (organism), cognitive (subfield)

Methods: Statistics, Smoothing, state filtering, decompositions, Machine learning, Preprocessing, Evoked potentials

MeSH: Bayes Theorem, Brain, Electroencephalography, Humans, Linear Models, Memory, Multivariate Analysis

Journal subjects: Research and Analysis Methods, Bioassays and Physiological Analysis, Electrophysiological Techniques, Brain Electrophysiology, Electroencephalography, Biology and Life Sciences, Physiology, Electrophysiology, Neurophysiology, Neuroscience, Brain Mapping, Medicine and Health Sciences, Clinical Medicine, Clinical Neurophysiology, Imaging Techniques, Neuroimaging, Pharmacology, Drug Interactions, Event-Related Potentials, Physical Sciences, Mathematics, Probability Theory, Random Variables, Covariance, Simulation and Modeling, Functional Magnetic Resonance Imaging, Diagnostic Medicine, Diagnostic Radiology, Magnetic Resonance Imaging, Radiology and Imaging, Cognitive Science, Cognitive Psychology, Learning, Psychology, Social Sciences, Learning and Memory, Research Design, Experimental Design, Factorial Design

Topic: Statistical Methods and Applications (Statistics and Probability, Mathematics), according to OpenAlex

Funding: Birmingham City University; Max-Planck-Institut für Kognitions- und Neurowissenschaften

Citations: not cited yet (Europe PMC); 64 references in the paper

Abstract

Factorial designs are a mainstay of the scientific paradigm, allowing the effects of multiple experimental factors and their interactions to be efficiently studied within a single experiment. In brain imaging, however, multivariate data analyses commonly proceed using multivariate decoding and we argue that the standard “difference of accuracies” test is not a true test of interactions. To remedy this situation we propose an encoding method based on a Bayesian multivariate linear model which is ideally suited to the factorial analysis of such data. We show how it can be used to test for multivariate main effects and interactions using data from EEG studies of reward learning and declarative memory. This approach additionally allows for null hypotheses to be accepted and allows one to infer whether multivariate effects are driven by collections of univariate effects or voxel dependencies. We also propose that those wishing to pursue tests for interactions using decoding methods use an “accuracy of differences” test.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above, with 12 matches between paragraphs and lines of code.

wpennyUEA/MLC

License: none: the authors keep all their rights

State: the link answers, verified on 12 November 2026

Evidence: files inventoried

Commit: 60e6affb5daba82583d309292ef031accf1ad5b1, 17 November 2025

Languages: MATLAB (131), C (2)

Size: 154 files, 133 scripts

Software Heritage: not archived

Found in: “Data Availability”

Holds: README

Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: SPM (38 files), Statistics and Machine Learning Toolbox (4 files)

Availability: 1 check, the latest on 12 November 2026: the link answers

12 November 2026: the link answers

134 files

confplot/confidence_plot_test.m, MATLAB, 19 lines
confplot/confplot.m, MATLAB, 84 lines
data/gen_heterogeneous_data.m, MATLAB, 135 lines
data/gen_interaction_data.m, MATLAB, 146 lines
data/get_DM_data.m, MATLAB, 79 lines
data/get_reward_data.m, MATLAB, 149 lines, 1 match
data/get_synth_data.m, MATLAB, 38 lines
linear-regression/Contents.m, MATLAB, 57 lines
linear-regression/bayes_glinear_estimate.m, MATLAB, 96 lines, 1 match
linear-regression/bayes_glinear_test.m, MATLAB, 36 lines
linear-regression/bayes_glm_anova1.m, MATLAB, 95 lines, 1 match
linear-regression/bayes_glm_regression.m, MATLAB, 106 lines, 2 matches
linear-regression/bayes_glm_ttest1.m, MATLAB, 33 lines
linear-regression/bayes_linear_estimate.m, MATLAB, 40 lines
linear-regression/bayes_linear_test.m, MATLAB, 34 lines
linear-regression/bayes_tlinear_estimate.m, MATLAB, 62 lines
linear-regression/bayes_tlinear_test.m, MATLAB, 37 lines
linear-regression/default-bayes-factors/Contents.m, MATLAB, 48 lines
linear-regression/default-bayes-factors/binombf.m, MATLAB, 17 lines
linear-regression/default-bayes-factors/corrbf.m, MATLAB, 14 lines
linear-regression/default-bayes-factors/corrbfrep.m, MATLAB, 13 lines
linear-regression/default-bayes-factors/t1smpbf.m, MATLAB, 23 lines
linear-regression/default-bayes-factors/t2smpbf.m, MATLAB, 23 lines
linear-regression/demo_anova1_chick_weights.m, MATLAB, 46 lines
linear-regression/demo_anova1_compare.m, MATLAB, 54 lines
linear-regression/demo_anova1_confounds.m, MATLAB, 38 lines
linear-regression/demo_glm_test_hypothesis.m, MATLAB, 37 lines
linear-regression/demo_regression.m, MATLAB, 90 lines
linear-regression/demo_tlinear.m, MATLAB, 39 lines
linear-regression/demo_ttest_arbitrary_scale.m, MATLAB, 50 lines
linear-regression/demo_ttest_standard_scale.m, MATLAB, 65 lines
linear-regression/glm_anova1.m, MATLAB, 70 lines
linear-regression/glm_test_hypothesis.m, MATLAB, 40 lines
linear-regression/linregbf.m, MATLAB, 38 lines
linear-regression/linregbf_test.m, MATLAB, 30 lines
linear-regression/make_anova_design.m, MATLAB, 39 lines
misc/Contents.m, MATLAB, 31 lines
misc/auc_ranksum.m, MATLAB, 21 lines
misc/correlation_entropy_test.m, MATLAB, 20 lines
misc/demo_svm_classify.m, MATLAB, 17 lines
misc/gaussian_entropy.m, MATLAB, 11 lines
misc/get_corr_entropy.m, MATLAB, 26 lines
misc/line_search.m, MATLAB, 46 lines
misc/logmvNpdf.m, MATLAB, 40 lines
misc/logmvNpdf_robust.m, MATLAB, 41 lines
misc/mci_bernoulli_rnd.m, MATLAB, 12 lines
misc/mci_logit.m, MATLAB, 7 lines
misc/mci_sigmoid.m, MATLAB, 7 lines
misc/mci_smooth.m, MATLAB, 26 lines
misc/mci_softmax.m, MATLAB, 16 lines
misc/rdiv.m, MATLAB, 17 lines
misc/rfx_bms.m, MATLAB, 210 lines
misc/rsum.m, MATLAB, 10 lines
misc/savage_dickey_vector.m, MATLAB, 41 lines, 2 matches
misc/sensitivity_pcut.m, MATLAB, 28 lines
misc/svm_classify.m, MATLAB, 45 lines, 1 match
misc/svm_classify_old.m, MATLAB, 115 lines, 1 match
misc/test_spm_gamrnd.m, MATLAB, 15 lines
misc/zmuv.m, MATLAB, 17 lines
run_analyses.m, MATLAB, 98 lines
set_mlc_path.m, MATLAB, 8 lines
spm-code/Contents.m, MATLAB, 12 lines
spm-code/spm_BMS_bor.m, MATLAB, 97 lines
spm-code/spm_Bcdf.m, MATLAB, 91 lines
spm-code/spm_Bpdf.m, MATLAB, 92 lines
spm-code/spm_Dpdf.m, MATLAB, 36 lines
spm-code/spm_FcUtil.m, MATLAB, 933 lines
spm-code/spm_Fcdf.m, MATLAB, 119 lines
spm-code/spm_Gcdf.m, MATLAB, 100 lines
spm-code/spm_Ncdf.m, MATLAB, 93 lines
spm-code/spm_Npdf.m, MATLAB, 85 lines
spm-code/spm_SpUtil.m, MATLAB, 737 lines
spm-code/spm_ancova.m, MATLAB, 89 lines
spm-code/spm_cat.c, C, 640 lines
spm-code/spm_cat.m, MATLAB, 100 lines
spm-code/spm_cat_struct.m, MATLAB, 42 lines
spm-code/spm_dctmtx.m, MATLAB, 75 lines
spm-code/spm_diff.m, MATLAB, 171 lines
spm-code/spm_dirichlet_exceedance.m, MATLAB, 63 lines
spm-code/spm_eeg_morlet.m, MATLAB, 51 lines
spm-code/spm_funcheck.m, MATLAB, 40 lines
spm-code/spm_gamrnd.c, C, 121 lines
spm-code/spm_gamrnd.m, MATLAB, 25 lines
spm-code/spm_inv.m, MATLAB, 30 lines
spm-code/spm_invBcdf.m, MATLAB, 123 lines
spm-code/spm_invGcdf.m, MATLAB, 139 lines
spm-code/spm_invNcdf.m, MATLAB, 105 lines
spm-code/spm_invXcdf.m, MATLAB, 58 lines
spm-code/spm_kl_dirichlet.m, MATLAB, 32 lines
spm-code/spm_kl_eig_normal.m, MATLAB, 32 lines
spm-code/spm_kl_gamma.m, MATLAB, 20 lines
spm-code/spm_kl_normal.m, MATLAB, 29 lines
spm-code/spm_kl_normal_wishart.m, MATLAB, 29 lines
spm-code/spm_kl_normald.m, MATLAB, 40 lines
spm-code/spm_kl_wishart.m, MATLAB, 43 lines
spm-code/spm_length.m, MATLAB, 50 lines
spm-code/spm_lg_gamma.m, MATLAB, 27 lines
spm-code/spm_logdet.m, MATLAB, 74 lines
spm-code/spm_make_contrasts.m, MATLAB, 96 lines
spm-code/spm_multrnd.m, MATLAB, 19 lines
spm-code/spm_mvNpdf.m, MATLAB, 70 lines
spm-code/spm_mvtpdf.m, MATLAB, 30 lines
spm-code/spm_normrnd.m, MATLAB, 32 lines
spm-code/spm_nwcov.m, MATLAB, 34 lines
spm-code/spm_nwpost.m, MATLAB, 45 lines
spm-code/spm_nwrnd.m, MATLAB, 46 lines
spm-code/spm_sp.m, MATLAB, 1,415 lines
spm-code/spm_svd.m, MATLAB, 95 lines
spm-code/spm_unvec.m, MATLAB, 89 lines
spm-code/spm_vec.m, MATLAB, 57 lines
spm-code/spm_wishrnd.m, MATLAB, 42 lines
toolbox/bayes_manova_period.m, MATLAB, 50 lines
toolbox/bayes_manova_space_time.m, MATLAB, 55 lines
toolbox/bayes_manova_time_series.m, MATLAB, 56 lines
toolbox/classic_manova.m, MATLAB, 47 lines
toolbox/classic_manova_time_series.m, MATLAB, 40 lines
toolbox/decode_time_series.m, MATLAB, 77 lines
toolbox/erp_baseline_correct.m, MATLAB, 46 lines
toolbox/mlm_nw.m, MATLAB, 75 lines
toolbox/plot_anova_map.m, MATLAB, 83 lines, 1 match
toolbox/plot_bman_results.m, MATLAB, 49 lines
toolbox/plot_classifier_results.m, MATLAB, 66 lines, 2 matches
toolbox/plot_cman_results.m, MATLAB, 55 lines
toolbox/plot_condition_means.m, MATLAB, 52 lines
toolbox/plot_scalp_map.m, MATLAB, 39 lines
toolbox/plot_scalp_map_details.m, MATLAB, 221 lines
toolbox/plot_univariate_effects.m, MATLAB, 21 lines
toolbox/ptm_contrast_range.m, MATLAB, 19 lines
toolbox/ptm_contrast_time.m, MATLAB, 8 lines
toolbox/ptm_fit_enc.m, MATLAB, 52 lines
toolbox/run_classifier.m, MATLAB, 29 lines
toolbox/spatial_precision_matrix.m, MATLAB, 26 lines
toolbox/stm_scale_data.m, MATLAB, 21 lines
README.md, Text, 15 lines

At the source: github.com/wpennyUEA/MLC

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

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

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1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
133 scripts, each with its path and the digest of its content;
12 matches between paragraphs of the paper and lines of the code (method lexical-v1);
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Data

No dataset and no data link were found in the paper.

Data Availability

A matlab implementation of MLC is provided in the GitHub archive https://github.com/wpennyUEA/MLC. Links to the empirical data for the Reward Learning and Declarative Memory experiments are provided in the README file in the GitHub archive.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 12 November 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 7 MeSH terms, 2 funders, 48 references.

Cite

This paper

Penny, W., Sambrook, T., & Renoult, L. (2026). Testing for interactions in multivariate data. PloS one, 21(11), e0338580. https://doi.org/10.1371/journal.pone.0338580

BibTeX

@article{penny2026testing, author = {Penny, Will and Sambrook, Tom and Renoult, Louis}, title = {{Testing for interactions in multivariate data}}, journal = {PloS one}, year = {2026}, month = nov, volume = {21}, number = {11}, pages = {e0338580}, publisher = {PLOS}, issn = {1932-6203}, doi = {10.1371/journal.pone.0338580}, url = {https://doi.org/10.1371/journal.pone.0338580}, pmid = {43008059}, pmcid = {PMC13750587} }

RIS

TY - JOUR AU - Penny, Will AU - Sambrook, Tom AU - Renoult, Louis TI - Testing for interactions in multivariate data T2 - PloS one J2 - PLoS One PY - 2026 DA - 2026/11/10 VL - 21 IS - 11 SP - e0338580 SN - 1932-6203 PB - PLOS DO - 10.1371/journal.pone.0338580 UR - https://doi.org/10.1371/journal.pone.0338580 LA - en ER -

CSL-JSON

{ "id": "10.1371/journal.pone.0338580", "type": "article-journal", "title": "Testing for interactions in multivariate data", "container-title": "PloS one", "author": [ { "family": "Penny", "given": "Will" }, { "family": "Sambrook", "given": "Tom" }, { "family": "Renoult", "given": "Louis" } ], "container-title-short": "PLoS One", "volume": "21", "issue": "11", "page": "e0338580", "DOI": "10.1371/journal.pone.0338580", "PMID": "43008059", "PMCID": "PMC13750587", "ISSN": "1932-6203", "publisher": "PLOS", "URL": "https://doi.org/10.1371/journal.pone.0338580", "language": "en", "issued": { "date-parts": [ [ 2026, 11, 10 ] ] } }

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