{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,7]],"date-time":"2026-10-07T22:51:12Z","timestamp":1791413472798,"version":"4.3.3"},"reference-count":23,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T00:00:00Z","timestamp":1635120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,8,24]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Factorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism while conditioning on the potential outcomes. To this end, we derive the sampling properties of the regression estimators under a wide range of specifications, and establish the appropriateness of the corresponding robust standard errors for Wald-type inference. The results help to clarify the causal interpretation of the coefficients in these factor-based regressions, and motivate the definition of general factorial effects to unify the definitions of factorial effects in various fields. We also quantify the bias-variance trade-off between the saturated and unsaturated regressions from the design-based perspective.<\/jats:p>","DOI":"10.1093\/biomet\/asab051","type":"journal-article","created":{"date-parts":[[2021,10,21]],"date-time":"2021-10-21T03:12:53Z","timestamp":1634785973000},"page":"799-815","source":"Crossref","is-referenced-by-count":26,"title":["Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties"],"prefix":"10.1093","volume":"109","author":[{"given":"Anqi","family":"Zhao","sequence":"first","affiliation":[{"name":"Department of Statistics and Data Science, National University of Singapore , 117546 Singapore"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peng","family":"Ding","sequence":"additional","affiliation":[{"name":"Department of Statistics, University of California, Berkeley , 425 Evans Hall, Berkeley, California 94720, U.S.A"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2021,10,25]]},"reference":[{"key":"2022082420280443300_B1","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1257\/0002828042002561","article-title":"Are Emily and Greg more employable than Lakisha and Jamal? 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