{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,5]],"date-time":"2026-05-05T00:17:49Z","timestamp":1777940269647,"version":"3.51.4"},"reference-count":25,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T00:00:00Z","timestamp":1574380800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Statistical Modelling"],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p>In regression analysis, the data sample is often composed of diverse sub-populations such as ethnicities and geographical regions. In multiple application areas, it is important to identify the groups where each covariate has a positive, negative or null impact on the response. If the number of sub-populations is small, a full interaction model may be fit with group-specific covariate effects. However, if the number of groups is very large, for example, hospitals or other clustering units, such a model is not identifiable. Therefore, we propose a prior distribution which combines the information across sub-populations with a similar covariate effect. This Bayesian analysis of differential effects (BADE) classifies the group-specific covariate effects as positive, negative or null. Besides allowing the analysis of differential effects for many sub-populations, the proposed approach improves substantially the identification of important interactions in cases with few groups. This is illustrated via simulations. The procedure is motivated on, and applied to, a large study related to patients\u2019 satisfaction with hospitals, where we show that classifying group-specific covariate effects based on methods such as mixed-effects models may be strongly misleading.<\/jats:p>","DOI":"10.1177\/1471082x19881844","type":"journal-article","created":{"date-parts":[[2019,11,23]],"date-time":"2019-11-23T00:34:37Z","timestamp":1574469277000},"page":"244-263","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Bayesian analysis of differential effects in multi-group regression methods"],"prefix":"10.1177","volume":"21","author":[{"given":"Adrian","family":"Quintero","sequence":"first","affiliation":[{"name":"I-BioStat, KU Leuven, Leuven, Belgium."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Geert","family":"Verbeke","sequence":"additional","affiliation":[{"name":"I-BioStat, KU Leuven, Leuven, Belgium."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luk","family":"Bruyneel","sequence":"additional","affiliation":[{"name":"Department of Public Health and Primary Care, KU Leuven, Leuven, Belgium."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Emmanuel","family":"Lesaffre","sequence":"additional","affiliation":[{"name":"I-BioStat, KU Leuven, Leuven, Belgium."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2019,11,22]]},"reference":[{"key":"bibr1-1471082X19881844","doi-asserted-by":"crossref","unstructured":"Barbieri MM, Berger JO (2003) Optimal predictive model selection.\n                      The Annals of Statistics\n                      , 32, 870\u201397.","DOI":"10.1214\/009053604000000238"},{"key":"bibr2-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/44.3-4.533"},{"key":"bibr3-1471082X19881844","first-page":"41","volume":"17","author":"Boulding W","year":"2011","journal-title":"The American Journal of Managed Care"},{"key":"bibr4-1471082X19881844","volume-title":"Bayes and Empirical Bayes Methods for Data Analysis, 2nd edition","author":"Carlin B","year":"1996"},{"key":"bibr5-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1007\/s10142-007-0058-3"},{"key":"bibr6-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1111\/j.1475-6773.2005.00490.x"},{"key":"bibr7-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.2307\/2532645"},{"key":"bibr8-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1214\/06-BA117A"},{"key":"bibr9-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1080\/19345747.2011.618213"},{"key":"bibr10-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1198\/016214505000000051"},{"key":"bibr11-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1002\/9781119942412"},{"key":"bibr12-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.201600064"},{"key":"bibr13-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1988.10478694"},{"key":"bibr14-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.2307\/1924426"},{"key":"bibr15-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9868.00358"},{"key":"bibr16-1471082X19881844","author":"Plummer M.","year":"2013","journal-title":"JAGS User Manual"},{"key":"bibr17-1471082X19881844","doi-asserted-by":"publisher","DOI":"10.1002\/sim.1296"},{"key":"bibr18-1471082X19881844","unstructured":"R Core Team (2018) R: A Language and Environment for Statistical Computing. 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