{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T02:01:42Z","timestamp":1782266502174,"version":"3.54.5"},"reference-count":56,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T00:00:00Z","timestamp":1677715200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,11,15]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Calibration weighting has been widely used to correct selection biases in nonprobability sampling, missing data and causal inference. The main idea is to calibrate the biased sample to the benchmark by adjusting the subject weights. However, hard calibration can produce enormous weights when an exact calibration is enforced on a large set of extraneous covariates. This article proposes a soft calibration scheme, where the outcome and the selection indicator follow mixed-effect models. The scheme imposes an exact calibration on the fixed effects and an approximate calibration on the random effects. On the one hand, our soft calibration has an intrinsic connection with best linear unbiased prediction, which results in a more efficient estimation compared to hard calibration. On the other hand, soft calibration weighting estimation can be envisioned as penalized propensity score weight estimation, with the penalty term motivated by the mixed-effect structure. The asymptotic distribution and a valid variance estimator are derived for soft calibration. We demonstrate the superiority of the proposed estimator over other competitors in simulation studies and using a real-world data application on the effect of BMI screening on childhood obesity.<\/jats:p>","DOI":"10.1093\/biomet\/asad016","type":"journal-article","created":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T22:39:24Z","timestamp":1677710364000},"page":"897-911","source":"Crossref","is-referenced-by-count":8,"title":["Soft calibration for selection bias problems under mixed-effects models"],"prefix":"10.1093","volume":"110","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3850-5587","authenticated-orcid":false,"given":"Chenyin","family":"Gao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7703-707X","authenticated-orcid":false,"given":"Shu","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Statistics, North Carolina State University , 2311 Stinson Drive , Raleigh, North Carolina 27695, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0246-6029","authenticated-orcid":false,"given":"Jae Kwang","family":"Kim","sequence":"additional","affiliation":[{"name":"Department of Statistics, Iowa State University , 2438 Osborn Dr, Ames, Iowa 50011, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2023,3,2]]},"reference":[{"key":"2023111615233675900_asad016-B1","first-page":"211","article-title":"Decomposition of gender wage inequalities through calibration: application to the swiss structure of earnings survey","volume":"43","author":"Anastasiade","year":"2017","journal-title":"Survey Methodol"},{"key":"2023111615233675900_asad016-B2","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1111\/rssb.12268","article-title":"Approximate residual balancing: debiased inference of average treatment effects in high dimensions","volume":"80","author":"Athey","year":"2018","journal-title":"J. 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