{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,30]],"date-time":"2026-06-30T21:52:07Z","timestamp":1782856327246,"version":"3.54.5"},"reference-count":92,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2025,4,15]],"date-time":"2025-04-15T00:00:00Z","timestamp":1744675200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":["bpspsychub.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Brit J Math &amp; Statis"],"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Distinguishing cause from effect \u2013 that is, determining whether <jats:italic>x<\/jats:italic> causes <jats:italic>y<\/jats:italic> (<jats:italic>x<\/jats:italic>\u2009\u2192\u2009<jats:italic>y<\/jats:italic>) or, alternatively, whether <jats:italic>y<\/jats:italic> causes <jats:italic>x<\/jats:italic> (<jats:italic>y<\/jats:italic>\u2009\u2192\u2009<jats:italic>x<\/jats:italic>) \u2013 is a primary research goal in many psychological research areas. Despite its importance, determining causal direction with observational data remains a difficult task. In this study, we introduce an independence\u2010based approach for causal discovery between two variables of interest under a linear non\u2010Gaussian model framework. We propose a two\u2010step algorithm based on distance correlations that provides empirical conclusions on the <jats:italic>causal directionality<\/jats:italic> of effects under realistic conditions typically seen in psychological studies, that is, in the presence of hidden confounders. The performance of the proposed algorithm is evaluated using Monte\u2010Carlo simulations. Findings suggest that the algorithm can effectively detect the causal direction between two variables of interest, even in the presence of weak hidden confounders. Moreover, distance correlations provide useful insights into the magnitude of hidden confounding. We provide an empirical example to demonstrate the application of our proposed approach and discuss practical implications and future directions.<\/jats:p>","DOI":"10.1111\/bmsp.12391","type":"journal-article","created":{"date-parts":[[2025,4,16]],"date-time":"2025-04-16T00:25:51Z","timestamp":1744763151000},"page":"965-995","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Distinguishing cause from effect in psychological research: An independence\u2010based approach under linear non\u2010Gaussian models"],"prefix":"10.1111","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4120-6756","authenticated-orcid":false,"given":"Dexin","family":"Shi","sequence":"first","affiliation":[{"name":"Department of Psychology University of South Carolina  Columbia South Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Bo","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Labor and Employment Relations University of Illinois Urbana\u2010Champaign  Champaign Illinois USA"},{"name":"Department of Psychology University of Illinois Urbana\u2010Champaign  Champaign Illinois USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6468-905X","authenticated-orcid":false,"given":"Wolfgang","family":"Wiedermann","sequence":"additional","affiliation":[{"name":"Department of Educational School, and Counseling Psychology University of Missouri  Columbia Missouri USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Amanda J.","family":"Fairchild","sequence":"additional","affiliation":[{"name":"Department of Psychology University of South Carolina  Columbia South Carolina USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,4,15]]},"reference":[{"key":"e_1_2_14_2_1","doi-asserted-by":"publisher","DOI":"10.4135\/9781412984744"},{"key":"e_1_2_14_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/11626891"},{"key":"e_1_2_14_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1996.10476902"},{"key":"e_1_2_14_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.leaqua.2022.101673"},{"key":"e_1_2_14_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11747\u2010021\u201000805\u2010y"},{"key":"e_1_2_14_7_1","doi-asserted-by":"publisher","DOI":"10.1086\/690946"},{"key":"e_1_2_14_8_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0026739"},{"key":"e_1_2_14_9_1","doi-asserted-by":"publisher","DOI":"10.4135\/9781412985321"},{"key":"e_1_2_14_10_1","doi-asserted-by":"publisher","DOI":"10.1027\/1614\u20102241\/a000057"},{"key":"e_1_2_14_11_1","doi-asserted-by":"publisher","DOI":"10.1006\/jrpe.2000.2302"},{"key":"e_1_2_14_12_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428\u2010016\u20100814\u20101"},{"key":"e_1_2_14_13_1","doi-asserted-by":"crossref","unstructured":"Chen W. Huang Z. Cai R. Hao Z. &Zhang K.(2024).Identification of causal structure with latent variables based on higher order cumulants. In proceedings of the AAAI conference on artificial intelligence (38 18 pp. 20353\u201320361).","DOI":"10.1609\/aaai.v38i18.30017"},{"key":"e_1_2_14_14_1","doi-asserted-by":"publisher","DOI":"10.1177\/00491241221099"},{"key":"e_1_2_14_15_1","volume-title":"Statistical power analysis for the behavioral sciences","author":"Cohen J.","year":"1988"},{"key":"e_1_2_14_16_1","doi-asserted-by":"publisher","DOI":"10.2307\/2136404"},{"key":"e_1_2_14_17_1","doi-asserted-by":"publisher","DOI":"10.1017\/jmo.2015.15"},{"key":"e_1_2_14_18_1","doi-asserted-by":"publisher","DOI":"10.1037\/0021\u20109010.90.6.1241"},{"key":"e_1_2_14_19_1","doi-asserted-by":"publisher","DOI":"10.2307\/1401511"},{"key":"e_1_2_14_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610920008832589"},{"key":"e_1_2_14_21_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev\u2010soc\u2010071913\u2010043455"},{"key":"e_1_2_14_22_1","unstructured":"Entner D. Hoyer P. &Spirtes P.(2012).Statistical test for consistent estimation of causal effects in linear non\u2010Gaussian models. In Artificial intelligence and statistics (pp. 364\u2013372). PMLR."},{"key":"e_1_2_14_23_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000414"},{"key":"e_1_2_14_24_1","doi-asserted-by":"publisher","DOI":"10.4135\/9781412983594"},{"key":"e_1_2_14_25_1","doi-asserted-by":"publisher","DOI":"10.1177\/25152459221120217"},{"key":"e_1_2_14_26_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.smrv.2021.101565"},{"key":"e_1_2_14_27_1","unstructured":"Gretton A. Fukumizu K. Teo C. H. Song L. Scholkopf B. &Smola A. J.(2008).A kernel statistical test of independence. Advances in Neural Information Processing Systems 20 585\u2013592."},{"key":"e_1_2_14_28_1","doi-asserted-by":"publisher","DOI":"10.1177\/17456916209215"},{"key":"e_1_2_14_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dcn.2020.100867"},{"key":"e_1_2_14_30_1","doi-asserted-by":"publisher","DOI":"10.1353\/obs.2020.0000"},{"key":"e_1_2_14_31_1","first-page":"267","volume-title":"Research in organizational behavior","author":"Hunter J. E.","year":"1982"},{"key":"e_1_2_14_32_1","doi-asserted-by":"publisher","DOI":"10.1002\/0471221317"},{"key":"e_1_2_14_33_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/36.1\u20102.149"},{"key":"e_1_2_14_34_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev\u2010clinpsy\u2010032210\u2010104540"},{"key":"e_1_2_14_35_1","doi-asserted-by":"publisher","DOI":"10.1136\/bmjopen\u20102015\u2010007765"},{"key":"e_1_2_14_36_1","doi-asserted-by":"publisher","DOI":"10.1037\/apl0000169"},{"key":"e_1_2_14_37_1","doi-asserted-by":"publisher","DOI":"10.1037\/1082\u2010989x.7.1.83"},{"key":"e_1_2_14_38_1","doi-asserted-by":"publisher","DOI":"10.1037\/met0000226"},{"key":"e_1_2_14_39_1","doi-asserted-by":"publisher","DOI":"10.1037\/\/0033\u20102909.105.1.156"},{"issue":"1","key":"e_1_2_14_40_1","first-page":"1103","article-title":"Distinguishing cause from effect using observational data: Methods and benchmarks","volume":"17","author":"Mooij J. M.","year":"2016","journal-title":"The Journal of Machine Learning Research"},{"key":"e_1_2_14_41_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012031"},{"key":"e_1_2_14_42_1","doi-asserted-by":"publisher","DOI":"10.1177\/0963721413492763"},{"key":"e_1_2_14_43_1","doi-asserted-by":"crossref","unstructured":"Park K. Waldorp L. &Ryan O.(2023).Discovering cyclic causal models in psychological research.https:\/\/doi.org\/10.31234\/osf.io\/qb9t3","DOI":"10.31234\/osf.io\/qb9t3"},{"key":"e_1_2_14_44_1","doi-asserted-by":"publisher","DOI":"10.1287\/mksc.1120.0718"},{"key":"e_1_2_14_45_1","doi-asserted-by":"publisher","DOI":"10.1016\/0004\u20103702(86)90072\u2010X"},{"key":"e_1_2_14_46_1","volume-title":"Probabilistic reasoning in intelligent systems: Networks of plausible inference","author":"Pearl J.","year":"1988"},{"key":"e_1_2_14_47_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803161"},{"key":"e_1_2_14_48_1","doi-asserted-by":"publisher","DOI":"10.1002\/job.336"},{"key":"e_1_2_14_49_1","first-page":"2009","article-title":"Causal discovery with continuous additive noise models","volume":"15","author":"Peters J.","year":"2014","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_14_50_1","unstructured":"Pollaris A. &Bontempi G.(2020).Latent Causation: An algorithm for pairs of correlated latent variables in linear non\u2010Gaussian structural equation modeling. In Cao L. Kosters W. and Lijffijt J. (eds.) BNAIC\/BENELEARN 2020: Proceedings of the 32nd Benelux Conference on Artificial Intelligence (BNAIC 2020) and the 29th Belgian\u2013Dutch Conference on Machine Learning (Benelearn 2020) pp. 209\u2013223."},{"key":"e_1_2_14_51_1","doi-asserted-by":"publisher","DOI":"10.1177\/0165025412448944"},{"key":"e_1_2_14_52_1","volume-title":"R: A language and environment for statistical computing","author":"R Core Team","year":"2023"},{"key":"e_1_2_14_53_1","unstructured":"Rizzo M. L. Szekely G. J. &Rizzo M. M.(2022).energy: E\u2010statistics: Multivariate inference via the energy of data. R package version 1.7\u201012.https:\/\/cran.r\u2010project.org\/web\/packages\/energy\/index.html"},{"key":"e_1_2_14_54_1","doi-asserted-by":"publisher","DOI":"10.21236\/ada114514"},{"key":"e_1_2_14_55_1","doi-asserted-by":"publisher","DOI":"10.1037\/h0037350"},{"key":"e_1_2_14_56_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1177012032"},{"key":"e_1_2_14_57_1","doi-asserted-by":"publisher","DOI":"10.1037\/1076\u20108998.10.4.363"},{"key":"e_1_2_14_58_1","doi-asserted-by":"publisher","DOI":"10.1037\/0022\u2010006x.71.5.890"},{"key":"e_1_2_14_59_1","doi-asserted-by":"publisher","DOI":"10.1177\/0013164413487738"},{"key":"e_1_2_14_60_1","doi-asserted-by":"publisher","DOI":"10.1080\/10618600.2021.1938585"},{"key":"e_1_2_14_61_1","doi-asserted-by":"publisher","DOI":"10.1037\/a0023322"},{"key":"e_1_2_14_62_1","doi-asserted-by":"crossref","unstructured":"Shi D. Fairchild A. J. &Wiedermann W.(2023).One step at a time: A statistical approach for distinguishing mediators confounders and colliders using direction dependence analysis.Psychological Methods. Advance online publication.https:\/\/doi.org\/10.1037\/met0000619","DOI":"10.1037\/met0000619"},{"key":"e_1_2_14_63_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11121\u2010018\u20100901\u2010x"},{"key":"e_1_2_14_64_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-4-431-55784-5"},{"issue":"10","key":"e_1_2_14_65_1","first-page":"2003","article-title":"A linear non\u2010Gaussian acyclic model for causal discovery","volume":"7","author":"Shimizu S.","year":"2006","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_14_66_1","first-page":"1225","article-title":"DirectLiNGAM: A direct method for learning a linear non\u2010Gaussian structural equation model","volume":"12","author":"Shimizu S.","year":"2011","journal-title":"Journal of Machine Learning Research"},{"key":"e_1_2_14_67_1","first-page":"217","article-title":"On a property of the normal distribution","volume":"89","author":"Skitovich W. P.","year":"1953","journal-title":"Doklady Akademii Nauk SSSR [Reports of the Academy of Sciences USSR]"},{"key":"e_1_2_14_68_1","doi-asserted-by":"publisher","DOI":"10.1037\/pspp0000096"},{"key":"e_1_2_14_69_1","doi-asserted-by":"publisher","DOI":"10.1007\/bf00929796"},{"key":"e_1_2_14_70_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1464\u20100597.2009.00414.x"},{"key":"e_1_2_14_71_1","doi-asserted-by":"publisher","DOI":"10.7551\/mitpress\/1754.001.0001"},{"key":"e_1_2_14_72_1","doi-asserted-by":"publisher","DOI":"10.1037\/hea0000577"},{"key":"e_1_2_14_73_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610920500201228"},{"key":"e_1_2_14_74_1","doi-asserted-by":"publisher","DOI":"10.1201\/9780429157158\u201019"},{"key":"e_1_2_14_75_1","doi-asserted-by":"publisher","DOI":"10.1214\/009053607000000505"},{"key":"e_1_2_14_76_1","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2011.540475"},{"key":"e_1_2_14_77_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.smrv.2021.101500"},{"key":"e_1_2_14_78_1","doi-asserted-by":"publisher","DOI":"10.1177\/0165025412439968"},{"key":"e_1_2_14_79_1","first-page":"183","volume-title":"Direction dependence in statistical modeling: Methods of analysis","author":"Eye A.","year":"2021"},{"key":"e_1_2_14_80_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.2014.993081"},{"key":"e_1_2_14_81_1","first-page":"81","volume-title":"Direction dependence in statistical modeling: Methods of analysis","author":"Wiedermann W.","year":"2021"},{"key":"e_1_2_14_82_1","doi-asserted-by":"publisher","DOI":"10.1007\/s41237\u2010021\u201000154\u20108"},{"key":"e_1_2_14_83_1","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2016.1275498"},{"key":"e_1_2_14_84_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428\u2010018\u20101031\u2010x"},{"key":"e_1_2_14_85_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428\u2010019\u201001230\u20104"},{"key":"e_1_2_14_86_1","first-page":"9","volume-title":"Direction dependence in statistical modeling: Methods of analysis","author":"Wiedermann W.","year":"2021"},{"key":"e_1_2_14_87_1","doi-asserted-by":"publisher","DOI":"10.1080\/00273171.2018.1528542"},{"key":"e_1_2_14_88_1","doi-asserted-by":"publisher","DOI":"10.1177\/0165025415582056"},{"key":"e_1_2_14_89_1","doi-asserted-by":"publisher","DOI":"10.1177\/109442819921005"},{"key":"e_1_2_14_90_1","doi-asserted-by":"publisher","DOI":"10.1177\/25152459221095823"},{"key":"e_1_2_14_91_1","doi-asserted-by":"publisher","DOI":"10.1037\/apl0000268"},{"key":"e_1_2_14_92_1","doi-asserted-by":"publisher","DOI":"10.1177\/10731911211008245"},{"key":"e_1_2_14_93_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428\u2010023\u201002217\u2010y"}],"container-title":["British Journal of Mathematical and Statistical Psychology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/bmsp.12391","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T05:47:33Z","timestamp":1760334453000},"score":1,"resource":{"primary":{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/10.1111\/bmsp.12391"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,15]]},"references-count":92,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["10.1111\/bmsp.12391"],"URL":"https:\/\/doi.org\/10.1111\/bmsp.12391","archive":["Portico"],"relation":{},"ISSN":["0007-1102","2044-8317"],"issn-type":[{"value":"0007-1102","type":"print"},{"value":"2044-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,4,15]]},"assertion":[{"value":"2024-07-15","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-03-30","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-04-15","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}