{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,17]],"date-time":"2026-05-17T02:04:59Z","timestamp":1778983499297,"version":"3.51.4"},"reference-count":55,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T00:00:00Z","timestamp":1731369600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["bpspsychub.onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Brit J Math &amp;amp; Statis"],"published-print":{"date-parts":[[2025,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Interaction analysis using linear regression is widely employed in psychology and related fields, yet it often induces confusion among applied researchers and students. This paper aims to address this confusion by developing intuitive visual explanations based on causal graphs. By leveraging causal graphs with distinct interaction nodes, we provide clear insights into interpreting main effects in the presence of interaction, the rationale behind centering to reduce multicollinearity, and other pertinent topics. The proposed graphical approach could serve as a useful complement to existing algebraic explanations, fostering a more comprehensive understanding of the mechanics of linear interaction analysis.<\/jats:p>","DOI":"10.1111\/bmsp.12369","type":"journal-article","created":{"date-parts":[[2024,11,12]],"date-time":"2024-11-12T07:24:28Z","timestamp":1731396268000},"page":"486-499","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Understanding linear interaction analysis with causal graphs"],"prefix":"10.1111","volume":"78","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6731-7123","authenticated-orcid":false,"given":"Yongnam","family":"Kim","sequence":"first","affiliation":[{"name":"Department of Education Seoul National University  Seoul Korea"},{"name":"Education Research Institute Seoul National University  Seoul Korea"},{"name":"Learning Sciences Research Institute Seoul National University  Seoul Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7398-4205","authenticated-orcid":false,"given":"Geryong","family":"Jung","sequence":"additional","affiliation":[{"name":"Department of Korean Language Education Seoul National University  Seoul Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,11,12]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1177\/1094428115627498"},{"key":"e_1_2_9_3_1","volume-title":"Multiple regression: Testing and interpreting interactions","author":"Aiken L. S.","year":"1991"},{"key":"e_1_2_9_4_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyac126"},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.2307\/2585577"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-007-6094-3_15"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1093\/pan\/mpi014"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1751\u20107893.2010.00177.x"},{"key":"e_1_2_9_9_1","unstructured":"Centellas M.(2016).Can I keep interaction term without original terms to avoid multicollinearity?https:\/\/www.researchgate.net\/post\/Can_I_keep_interaction_term_without_original_terms_to_avoid_multicollinearity"},{"key":"e_1_2_9_10_1","doi-asserted-by":"publisher","DOI":"10.2307\/2136512"},{"key":"e_1_2_9_11_1","volume-title":"Applied multiple regression\/correlation analysis for the behavioral sciences","author":"Cohen J.","year":"2003"},{"key":"e_1_2_9_12_1","doi-asserted-by":"publisher","DOI":"10.1515\/jci\u20102013\u20100021"},{"key":"e_1_2_9_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/3501714.3501745"},{"key":"e_1_2_9_14_1","first-page":"327","volume-title":"Heuristics, probability and causality: A tribute to Judea Pearl","author":"Elwert F.","year":"2010"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev\u2010soc\u2010071913\u2010043455"},{"key":"e_1_2_9_16_1","unstructured":"Goroshit M.(2015).Regression with interaction: Shall we look at the main effects?https:\/\/www.researchgate.net\/post\/Regression\u2010with\u2010interaction\u2010Shall\u2010we\u2010look\u2010at\u2010the\u2010main\u2010effects"},{"key":"e_1_2_9_17_1","doi-asserted-by":"publisher","DOI":"10.4135\/9781848608184"},{"key":"e_1_2_9_18_1","volume-title":"Introduction to mediation, moderation, and conditional process analysis: A regression\u2010based approach","author":"Hayes A. F.","year":"2013"},{"key":"e_1_2_9_19_1","volume-title":"Causal inference: What if","author":"Hern\u00e1n M. A.","year":"2020"},{"key":"e_1_2_9_20_1","volume-title":"Statistical methods for psychology","author":"Howell D. C.","year":"2012"},{"key":"e_1_2_9_21_1","unstructured":"Huang F. L.(2023).Why does centering reduce multicollinearity?https:\/\/francish.net\/post\/centering\u2010multicollinearity\/"},{"key":"e_1_2_9_22_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781003226055"},{"key":"e_1_2_9_23_1","doi-asserted-by":"publisher","DOI":"10.3758\/s13428\u2010015\u20100624\u2010x"},{"key":"e_1_2_9_24_1","doi-asserted-by":"publisher","DOI":"10.4135\/9781412984522"},{"key":"e_1_2_9_25_1","doi-asserted-by":"publisher","DOI":"10.1207\/s15327906mbr2504_4"},{"key":"e_1_2_9_26_1","doi-asserted-by":"publisher","DOI":"10.1017\/psrm.2020.12"},{"key":"e_1_2_9_27_1","doi-asserted-by":"publisher","DOI":"10.52041\/serj.v7i1.477"},{"key":"e_1_2_9_28_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1601-183X.2009.00561.x"},{"key":"e_1_2_9_29_1","doi-asserted-by":"publisher","DOI":"10.1111\/bmsp.12217"},{"key":"e_1_2_9_30_1","doi-asserted-by":"publisher","DOI":"10.1177\/0049124119826155"},{"key":"e_1_2_9_31_1","unstructured":"Kovanen M.(2010).Interaction without the main effects.http:\/\/www.phidot.org\/forum\/viewtopic.php?f=34&t=1452"},{"key":"e_1_2_9_32_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jclinepi.2019.05.005"},{"key":"e_1_2_9_33_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0003055403000753"},{"key":"e_1_2_9_34_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyaa211"},{"key":"e_1_2_9_35_1","doi-asserted-by":"publisher","DOI":"10.1177\/0013164418817801"},{"key":"e_1_2_9_36_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511803161"},{"key":"e_1_2_9_37_1","doi-asserted-by":"publisher","DOI":"10.1515\/jci\u20102013\u20100003"},{"key":"e_1_2_9_38_1","doi-asserted-by":"publisher","DOI":"10.1177\/0049124115600597"},{"key":"e_1_2_9_39_1","volume-title":"Causal inference in statistics: A primer","author":"Pearl J.","year":"2016"},{"key":"e_1_2_9_40_1","doi-asserted-by":"publisher","DOI":"10.1177\/2515245917745629"},{"key":"e_1_2_9_41_1","doi-asserted-by":"publisher","DOI":"10.1177\/25152459211007368"},{"key":"e_1_2_9_42_1","doi-asserted-by":"publisher","DOI":"10.1037\/0033\u20102909.105.1.143"},{"key":"e_1_2_9_43_1","doi-asserted-by":"publisher","DOI":"10.1111\/0022\u20103816.00012"},{"key":"e_1_2_9_44_1","unstructured":"Schubert M.(2017).Why could centering independent variables change the main effects with moderation?Cross Validated.https:\/\/stats.stackexchange.com\/q\/65898"},{"key":"e_1_2_9_45_1","doi-asserted-by":"publisher","DOI":"10.1177\/1094428108320370"},{"key":"e_1_2_9_46_1","doi-asserted-by":"publisher","DOI":"10.1111\/bmsp.12147"},{"key":"e_1_2_9_47_1","doi-asserted-by":"publisher","DOI":"10.1093\/ije\/dyy204"},{"key":"e_1_2_9_48_1","doi-asserted-by":"publisher","DOI":"10.1515\/jci\u20102016\u20100009"},{"key":"e_1_2_9_49_1","doi-asserted-by":"publisher","DOI":"10.1097\/ede.0b013e3181ba333c"},{"key":"e_1_2_9_50_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467\u20109868.2009.00728.x"},{"key":"e_1_2_9_51_1","unstructured":"Wachs S.(2017).Regression analysis only with interaction terms.https:\/\/www.researchgate.net\/post\/Regression\u2010Analysis\u2010only\u2010with\u2010interaction\u2010terms"},{"key":"e_1_2_9_52_1","doi-asserted-by":"publisher","DOI":"10.1186\/1752-4458-8-41"},{"key":"e_1_2_9_53_1","doi-asserted-by":"publisher","DOI":"10.1097\/EDE.0b013e318126c11d"},{"key":"e_1_2_9_54_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467\u20106494.1996.tb00813.x"},{"key":"e_1_2_9_55_1","first-page":"557","article-title":"Correlation and causation","volume":"20","author":"Wright S.","year":"1921","journal-title":"Journal of Agricultural Research"},{"key":"e_1_2_9_56_1","doi-asserted-by":"publisher","DOI":"10.1007\/s11205\u2010007\u20109143\u20101"}],"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.12369","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T11:05:25Z","timestamp":1761735925000},"score":1,"resource":{"primary":{"URL":"https:\/\/bpspsychub.onlinelibrary.wiley.com\/doi\/10.1111\/bmsp.12369"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,12]]},"references-count":55,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2025,5]]}},"alternative-id":["10.1111\/bmsp.12369"],"URL":"https:\/\/doi.org\/10.1111\/bmsp.12369","archive":["Portico"],"relation":{},"ISSN":["0007-1102","2044-8317"],"issn-type":[{"value":"0007-1102","type":"print"},{"value":"2044-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,12]]},"assertion":[{"value":"2024-04-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-10-22","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-11-12","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}