{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T05:10:28Z","timestamp":1776402628312,"version":"3.51.2"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1009659","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,2,8]],"date-time":"2022-02-08T00:00:00Z","timestamp":1644278400000}}],"reference-count":33,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T00:00:00Z","timestamp":1642982400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001665","name":"French National Research Agency","doi-asserted-by":"crossref","award":["ANR-10-BTBR-0001"],"award-info":[{"award-number":["ANR-10-BTBR-0001"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Since their introduction in the 50\u2019s, variance component mixed models have been widely used in many application fields. In this context, ReML estimation is by far the most popular procedure to infer the variance components of the model. Although many implementations of the ReML procedure are readily available, there is still need for computational improvements due to the ever-increasing size of the datasets to be handled, and to the complexity of the models to be adjusted. In this paper, we present a Min-Max (MM) algorithm for ReML inference and combine it with several speed-up procedures. The ReML MM algorithm we present is compared to 5 state-of-the-art publicly available algorithms used in statistical genetics. The computational performance of the different algorithms are evaluated on several datasets representing different plant breeding experimental designs. The MM algorithm ranks among the top 2 methods in almost all settings and is more versatile than many of its competitors. The MM algorithm is a promising alternative to the classical AI-ReML algorithm in the context of variance component mixed models. It is available in the <jats:monospace>MM4LMM<\/jats:monospace> R-package.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1009659","type":"journal-article","created":{"date-parts":[[2022,1,24]],"date-time":"2022-01-24T18:38:25Z","timestamp":1643049505000},"page":"e1009659","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":37,"title":["Efficient ReML inference in variance component mixed models using a Min-Max algorithm"],"prefix":"10.1371","volume":"18","author":[{"given":"Fabien","family":"Laporte","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6125-503X","authenticated-orcid":true,"given":"Alain","family":"Charcosset","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3839-9067","authenticated-orcid":true,"given":"Tristan","family":"Mary-Huard","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,1,24]]},"reference":[{"issue":"2","key":"pcbi.1009659.ref001","doi-asserted-by":"crossref","first-page":"226","DOI":"10.2307\/3001853","article-title":"Estimation of variance and covariance components","volume":"9","author":"CR Henderson","year":"1953","journal-title":"Biometrics"},{"key":"pcbi.1009659.ref002","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1214\/aoms\/1177728348","article-title":"A \u201cmixed model\u201d for the analysis of variance","author":"H Scheffe","year":"1956","journal-title":"The Annals of Mathematical Statistics"},{"key":"pcbi.1009659.ref003","first-page":"70","article-title":"Applications of mixed-effects models in biostatistics","author":"RD Gibbons","year":"2000","journal-title":"Sankhy\u0101: Indian J Stat, Series B"},{"issue":"4","key":"pcbi.1009659.ref004","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1071\/BI9560463","article-title":"Concept of general and specific combining ability in relation to diallel crossing systems","volume":"9","author":"B Griffing","year":"1956","journal-title":"Australian journal of biological sciences"},{"issue":"Symposium","key":"pcbi.1009659.ref005","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1093\/ansci\/1973.Symposium.10","article-title":"Sire evaluation and genetic trends","volume":"1973","author":"CR Henderson","year":"1973","journal-title":"Journal of Animal Science"},{"issue":"3","key":"pcbi.1009659.ref006","doi-asserted-by":"crossref","first-page":"1709","DOI":"10.1534\/genetics.107.080101","article-title":"Efficient control of population structure in model organism association mapping","volume":"178","author":"HM Kang","year":"2008","journal-title":"Genetics"},{"issue":"10","key":"pcbi.1009659.ref007","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1038\/nmeth.1681","article-title":"FaST linear mixed models for genome-wide association studies","volume":"8","author":"C Lippert","year":"2011","journal-title":"Nature methods"},{"issue":"7","key":"pcbi.1009659.ref008","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1038\/ng.2310","article-title":"Genome-wide efficient mixed-model analysis for association studies","volume":"44","author":"X Zhou","year":"2012","journal-title":"Nat genet"},{"issue":"1","key":"pcbi.1009659.ref009","first-page":"6","article-title":"Genome-wide data manipulation, association analysis and heritability estimates in R with Gaston 1.5","volume":"83","author":"C Dandine-Roulland","year":"2017","journal-title":"Human heredity"},{"issue":"2","key":"pcbi.1009659.ref010","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1038\/ng1702","article-title":"A unified mixed-model method for association mapping that accounts for multiple levels of relatedness","volume":"38","author":"J Yu","year":"2006","journal-title":"Nat Genet"},{"key":"pcbi.1009659.ref011","doi-asserted-by":"crossref","first-page":"1440","DOI":"10.2307\/2533274","article-title":"Average information REML: efficient algorithm for variance parameter estimation in linear mixed models","author":"AR Gilmour","year":"1995","journal-title":"Biometrics"},{"issue":"2","key":"pcbi.1009659.ref012","doi-asserted-by":"crossref","first-page":"449","DOI":"10.3168\/jds.S0022-0302(95)76654-1","article-title":"Restricted maximum likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information","volume":"78","author":"DL Johnson","year":"1995","journal-title":"Journal of dairy science"},{"key":"pcbi.1009659.ref013","unstructured":"Gilmour AR, Gogel BJ, Cullis BR, Welham S, Thompson R. 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