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The method is based on the rescaling bootstrap for multistage sampling introduced by Preston (Surv Methodol 35(2):227\u2013234, 2009). In his original version, this resampling method requires that the dataset includes only complete cases and no missing values. Thus, we propose two modifications for applying this method to nonresponse and imputation. These modifications are compared to other modifications in a Monte Carlo simulation study. The results of our simulation study show that our two proposed approaches are superior to the other modifications of the rescaling bootstrap and, in many situations, produce valid estimators for the variance of the imputed estimator in multistage sampling designs.<\/jats:p>","DOI":"10.1007\/s00180-021-01164-6","type":"journal-article","created":{"date-parts":[[2021,11,18]],"date-time":"2021-11-18T21:02:22Z","timestamp":1637269342000},"page":"1461-1494","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Applying the rescaling bootstrap under imputation for a multistage sampling design"],"prefix":"10.1007","volume":"37","author":[{"given":"Christian","family":"Bruch","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,11,18]]},"reference":[{"key":"1164_CR1","unstructured":"Alfons A, Filzmoser P, Hulliger B, Kolb J-P, Kraft S, M\u00fcnnich R, Templ M (2011) Synthetic data generation of silc data, Technical report, AMELI deliverable D6.2. https:\/\/www.uni-trier.de\/index.php?id=24676&L=2"},{"key":"1164_CR2","unstructured":"Bruch C (2016) Varianzsch\u00e4tzung unter Imputation und bei komplexen Stichprobendesigns, PhD thesis, Trier University. https:\/\/ubt.opus.hbz-nrw.de\/frontdoor\/index\/index\/year\/2016\/docId\/734"},{"issue":"4","key":"1164_CR3","doi-asserted-by":"publisher","first-page":"641","DOI":"10.1080\/00949655.2018.1563898","volume":"89","author":"C Bruch","year":"2019","unstructured":"Bruch C (2019) Applying the rescaling bootstrap under imputation: a simulation study. 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