{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T16:51:08Z","timestamp":1790095868268,"version":"4.0.1"},"reference-count":53,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"unspecified","delay-in-days":3502,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Psychometrika"],"published-print":{"date-parts":[[2015,6]]},"abstract":"<jats:p>A variety of statistical methods have been suggested for detecting differential item functioning (DIF) in the Rasch model. Most of these methods are designed for the comparison of pre-specified focal and reference groups, such as males and females. Latent class approaches, on the other hand, allow the detection of previously unknown groups exhibiting DIF. However, this approach provides no straightforward interpretation of the groups with respect to person characteristics. Here, we propose a new method for DIF detection based on model-based recursive partitioning that can be considered as a compromise between those two extremes. With this approach it is possible to detect groups of subjects exhibiting DIF, which are not pre-specified, but result from combinations of observed covariates. These groups are directly interpretable and can thus help generate hypotheses about the psychological sources of DIF. The statistical background and construction of the new method are introduced by means of an instructive example, and extensive simulation studies are presented to support and illustrate the statistical properties of the method, which is then applied to empirical data from a general knowledge quiz. A\u00a0software implementation of the method is freely available in the R system for statistical computing.<\/jats:p>","DOI":"10.1007\/s11336-013-9388-3","type":"journal-article","created":{"date-parts":[[2013,12,18]],"date-time":"2013-12-18T22:02:38Z","timestamp":1387404158000},"page":"289-316","source":"Crossref","is-referenced-by-count":117,"title":["Rasch Trees: A New Method for Detecting Differential Item Functioning in the Rasch Model"],"prefix":"10.1017","volume":"80","author":[{"given":"Carolin","family":"Strobl","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Julia","family":"Kopf","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Achim","family":"Zeileis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,1,1]]},"reference":[{"key":"S003331230000243X_CR32","doi-asserted-by":"publisher","DOI":"10.1007\/BF02295283"},{"key":"S003331230000243X_CR27","doi-asserted-by":"publisher","DOI":"10.1007\/BF02296272"},{"key":"S003331230000243X_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/bimj.200510191"},{"key":"S003331230000243X_CR51","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-9574.2007.00371.x"},{"key":"S003331230000243X_CR23","doi-asserted-by":"publisher","DOI":"10.1177\/0146621607312613"},{"key":"S003331230000243X_CR48","doi-asserted-by":"publisher","DOI":"10.3102\/10769986030004443"},{"key":"S003331230000243X_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02291180"},{"key":"S003331230000243X_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(02)00225-6"},{"key":"S003331230000243X_CR39","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v017.i05"},{"key":"S003331230000243X_CR25","unstructured":"Mair, P., Hatzinger, R., & Maier, M. (2012). eRm: extended Rasch modeling. R package version 0.15-0. http:\/\/CRAN.R-project.org\/package=eRm."},{"key":"S003331230000243X_CR18","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2008.00995.x"},{"key":"S003331230000243X_CR45","doi-asserted-by":"publisher","DOI":"10.1037\/a0016973"},{"key":"S003331230000243X_CR29","doi-asserted-by":"publisher","DOI":"10.1007\/s11336-012-9302-4"},{"key":"S003331230000243X_CR14","volume-title":"Advances in latent variable mixture models","author":"Hancock","year":"2007"},{"key":"S003331230000243X_CR38","doi-asserted-by":"publisher","DOI":"10.1037\/1082-989X.8.2.185"},{"key":"S003331230000243X_CR26","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/63.3.655"},{"key":"S003331230000243X_CR21","doi-asserted-by":"publisher","DOI":"10.2307\/2532406"},{"key":"S003331230000243X_CR41","doi-asserted-by":"publisher","DOI":"10.1177\/014662169001400305"},{"key":"S003331230000243X_CR37","volume-title":"R: a language and environment for statistical computing","year":"2012"},{"key":"S003331230000243X_CR6","volume-title":"Classification and regression trees","author":"Breiman","year":"1984"},{"key":"S003331230000243X_CR24","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v020.i09"},{"key":"S003331230000243X_CR34","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-3984.2007.00034.x"},{"key":"S003331230000243X_CR30","doi-asserted-by":"publisher","DOI":"10.2307\/2529881"},{"key":"S003331230000243X_CR15","doi-asserted-by":"publisher","DOI":"10.1002\/9780470316672"},{"key":"S003331230000243X_CR2","doi-asserted-by":"publisher","DOI":"10.2307\/2951764"},{"key":"S003331230000243X_CR53","unstructured":"Zeileis, A., Strobl, C., Wickelmaier, F., & Kopf, J. (2012). psychotree: recursive partitioning based on psychometric models. R package version 0.12-2. http:\/\/CRAN.R-project.org\/package=psychotree."},{"key":"S003331230000243X_CR12","doi-asserted-by":"publisher","DOI":"10.1023\/B:SOCI.0000025580.54702.90"},{"key":"S003331230000243X_CR46","doi-asserted-by":"publisher","DOI":"10.3102\/1076998609359791"},{"key":"S003331230000243X_CR8","first-page":"90","volume-title":"Proceedings of the seventeenth international conference on machine learning (ICML 2001)","author":"Dobra","year":"2001"},{"key":"S003331230000243X_CR36","doi-asserted-by":"publisher","DOI":"10.1007\/s11136-005-1551-6"},{"key":"S003331230000243X_CR4","volume-title":"Statistical theories of mental test scores","author":"Birnbaum","year":"1968"},{"key":"S003331230000243X_CR52","doi-asserted-by":"publisher","DOI":"10.1198\/106186008X319331"},{"key":"S003331230000243X_CR20","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-3984.1990.tb00751.x"},{"key":"S003331230000243X_CR33","doi-asserted-by":"publisher","DOI":"10.1017\/S1355617709990361"},{"key":"S003331230000243X_CR35","doi-asserted-by":"publisher","DOI":"10.1080\/08957340802558367"},{"key":"S003331230000243X_CR22","doi-asserted-by":"publisher","DOI":"10.1177\/014662169401800105"},{"key":"S003331230000243X_CR42","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-9473(03)00064-1"},{"key":"S003331230000243X_CR3","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-3984.1991.tb00341.x"},{"key":"S003331230000243X_CR43","first-page":"1","article-title":"The mixed Birnbaum model: estimation using collateral information","volume":"5","author":"Smit","year":"2000","journal-title":"Methods of Psychological Research Online"},{"key":"S003331230000243X_CR40","unstructured":"Rizopoulos, D. (2012). ltm: latent trait models under IRT. R package version 0.9-9. http:\/\/CRAN.R-project.org\/package=ltm."},{"key":"S003331230000243X_CR44","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2006.12.030"},{"key":"S003331230000243X_CR11","unstructured":"Fraley, C., & Raftery, A. (2012). mclust: Model-based clustering\/Normal mixture modeling. R package version 3.4.11. http:\/\/CRAN.R-project.org\/package=mclust."},{"key":"S003331230000243X_CR7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1745-3984.2005.00007"},{"key":"S003331230000243X_CR16","doi-asserted-by":"publisher","DOI":"10.1198\/106186006X133933"},{"key":"S003331230000243X_CR50","doi-asserted-by":"publisher","DOI":"10.1007\/s10862-008-9118-9"},{"key":"S003331230000243X_CR31","doi-asserted-by":"publisher","DOI":"10.1207\/s15327906mbr2104_5"},{"key":"S003331230000243X_CR10","doi-asserted-by":"publisher","DOI":"10.1198\/016214502760047131"},{"key":"S003331230000243X_CR49","doi-asserted-by":"publisher","DOI":"10.1007\/BF02294661"},{"key":"S003331230000243X_CR28","doi-asserted-by":"crossref","unstructured":"Merkle, E.C., Fan, J., & Zeileis, A. (2013). Testing for measurement invariance with respect to an ordinal variable. Psychometrika, forthcoming.","DOI":"10.1007\/s11336-013-9376-7"},{"key":"S003331230000243X_CR47","volume-title":"Allgemeinbildung in Deutschland\u2014Erkenntnisse aus dem SPIEGEL Studentenpisa-Test","author":"Trepte","year":"2010"},{"key":"S003331230000243X_CR13","doi-asserted-by":"publisher","DOI":"10.1111\/j.2044-8317.1980.tb00609.x"},{"key":"S003331230000243X_CR19","doi-asserted-by":"publisher","DOI":"10.1007\/BF01908075"},{"key":"S003331230000243X_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4230-7"}],"container-title":["Psychometrika"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11336-013-9388-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11336-013-9388-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S003331230000243X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,17]],"date-time":"2025-02-17T10:02:03Z","timestamp":1739786523000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S003331230000243X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6]]},"references-count":53,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2015,6]]}},"alternative-id":["S003331230000243X"],"URL":"https:\/\/doi.org\/10.1007\/s11336-013-9388-3","relation":{},"ISSN":["0033-3123","1860-0980"],"issn-type":[{"value":"0033-3123","type":"print"},{"value":"1860-0980","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6]]}}}