{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T01:21:37Z","timestamp":1792113697267,"version":"4.4.0"},"reference-count":15,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2019,7,24]],"date-time":"2019-07-24T00:00:00Z","timestamp":1563926400000},"content-version":"vor","delay-in-days":1,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,12,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>A within-cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size. Our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster. We then estimate the parameters by maximizing an average, over the bootstrap samples, of a suitable composite loglikelihood. The consistency of the proposed estimator is shown and does not require that the correct model for cluster size is specified. We give an estimator of the covariance matrix of the proposed estimator, and a test for the noninformativeness of the cluster sizes. A simulation study shows, as in Neuhaus &amp; McCulloch (2011), that the standard maximum likelihood estimator exhibits little bias for some regression coefficients. However, for those parameters which exhibit nonnegligible bias, the proposed method is successful in correcting for this bias.<\/jats:p>","DOI":"10.1093\/biomet\/asz035","type":"journal-article","created":{"date-parts":[[2019,6,10]],"date-time":"2019-06-10T19:14:20Z","timestamp":1560194060000},"page":"965-972","source":"Crossref","is-referenced-by-count":7,"title":["Within-cluster resampling for multilevel models under informative cluster size"],"prefix":"10.1093","volume":"106","author":[{"given":"D","family":"Lee","sequence":"first","affiliation":[{"name":"Department of Statistics, Iowa State University, 2438 Osborn Drive, Ames, Iowa 50011, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J K","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Statistics, Iowa State University, 2438 Osborn Drive, Ames, Iowa 50011, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"C J","family":"Skinner","sequence":"additional","affiliation":[{"name":"Department of Statistics, London School of Economics and Political Science, Houghton Street, London, WC2A 2AE, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2019,7,23]]},"reference":[{"key":"2020072220064026600_B1","doi-asserted-by":"crossref","first-page":"435","DOI":"10.1093\/biomet\/92.2.435","article-title":"Mean estimating equation approach to analysing cluster-correlated data with nonignorable cluster sizes","volume":"92","author":"Benhin,","year":"2005","journal-title":"Biometrika"},{"key":"2020072220064026600_B2","doi-asserted-by":"crossref","first-page":"1825","DOI":"10.1002\/sim.4239","article-title":"A joint modeling approach to data with informative cluster size: robustness to the cluster size model","volume":"30","author":"Chen,","year":"2011","journal-title":"Statist. 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