{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T00:57:15Z","timestamp":1774313835941,"version":"3.50.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T00:00:00Z","timestamp":1749427200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T00:00:00Z","timestamp":1749427200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/100013935","name":"Partnership for Clean Competition","doi-asserted-by":"publisher","award":["514"],"award-info":[{"award-number":["514"]}],"id":[{"id":"10.13039\/100013935","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013935","name":"Partnership for Clean Competition","doi-asserted-by":"publisher","award":["514"],"award-info":[{"award-number":["514"]}],"id":[{"id":"10.13039\/100013935","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100013935","name":"Partnership for Clean Competition","doi-asserted-by":"publisher","award":["514"],"award-info":[{"award-number":["514"]}],"id":[{"id":"10.13039\/100013935","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Stat Comput"],"published-print":{"date-parts":[[2025,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:p>Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and develop a optimisation-based inference schemes that can be applied to large data sets. An EM algorithm is proposed for the model with normal errors where the posterior distribution of the variable inclusion parameters is approximated using an Occam\u2019s window approach. Placing this approach within a variational Bayes scheme allows the algorithm to be extended to the model with skew-<jats:italic>t<\/jats:italic> errors. The performance of the algorithm is evaluated in a simulation study and applied to a longitudinal model for elite athlete performance in 100 metres track sprinting and weightlifting.<\/jats:p>","DOI":"10.1007\/s11222-025-10628-4","type":"journal-article","created":{"date-parts":[[2025,6,9]],"date-time":"2025-06-09T13:59:49Z","timestamp":1749477589000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Fast Bayesian inference in a class of sparse linear mixed effects models"],"prefix":"10.1007","volume":"35","author":[{"given":"Maria-Zafeiria","family":"Spyropoulou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James G.","family":"Hopker","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jim E.","family":"Griffin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,9]]},"reference":[{"key":"10628_CR1","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198505594.001.0001","volume-title":"Models for Repeated Measurements","author":"JK Lindsey","year":"1999","unstructured":"Lindsey, J.K.: Models for Repeated Measurements. Oxford University Press, Oxford (1999)"},{"key":"10628_CR2","doi-asserted-by":"publisher","DOI":"10.1201\/9781420011579","volume-title":"Longitudinal Data Analysis","author":"G Fitzmaurice","year":"2008","unstructured":"Fitzmaurice, G., Davidian, M., Verbeke, G., Molenberghs, G.: Longitudinal Data Analysis. CRC Press, Boca Raton (2008)"},{"key":"10628_CR3","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511755453","volume-title":"Semiparametric Regression","author":"D Ruppert","year":"2003","unstructured":"Ruppert, D., Wand, M.P., Carroll, R.J.: Semiparametric Regression. Cambridge University Press, Cambridge (2003)"},{"key":"10628_CR4","doi-asserted-by":"publisher","first-page":"762","DOI":"10.1111\/j.0006-341X.2003.00089.x","volume":"59","author":"Z Chen","year":"2003","unstructured":"Chen, Z., Dunson, D.B.: Random effects selection in linear mixed models. Biometrics 59, 762\u2013769 (2003)","journal-title":"Biometrics"},{"key":"10628_CR5","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.1016\/j.spl.2011.02.029","volume":"81","author":"A Armagan","year":"2011","unstructured":"Armagan, A., Dunson, D.B.: Sparse variational analysis of linear mixed models for large data sets. Statistics and Probability Letters 81, 1056\u20131062 (2011)","journal-title":"Statistics and Probability Letters"},{"key":"10628_CR6","doi-asserted-by":"publisher","first-page":"530","DOI":"10.1080\/03610918.2017.1387663","volume":"48","author":"DT Tung","year":"2019","unstructured":"Tung, D.T., Tran, M.-N., Cuong, T.M.: Bayesian adaptive lasso with variational bayes for variable selection in high-dimensional generalized linear mixed models. Communications in Statistics - Simulation and Computation 48, 530\u2013543 (2019)","journal-title":"Communications in Statistics - Simulation and Computation"},{"key":"10628_CR7","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1198\/016214508000000337","volume":"103","author":"T Park","year":"2008","unstructured":"Park, T., Casella, G.: The Bayesian Lasso. Journal of the American Statistical Association 103, 681\u2013686 (2008)","journal-title":"Journal of the American Statistical Association"},{"key":"10628_CR8","doi-asserted-by":"publisher","first-page":"5182","DOI":"10.1214\/22-EJS2063","volume":"16","author":"E Degani","year":"2022","unstructured":"Degani, E., Maestrini, L., Toczydlowska, D., Wand, M.P.: Sparse linear mixed model selection via streamlined variational Bayes. Electronic Journal of Statistics 16, 5182\u20135225 (2022)","journal-title":"Electronic Journal of Statistics"},{"key":"10628_CR9","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1214\/19-STS700","volume":"34","author":"A Bhadra","year":"2019","unstructured":"Bhadra, A., Datta, J., Polson, N.G., Willard, B.T.: Lasso meets horseshoe: a survey. Statistical Science 34, 405\u2013427 (2019)","journal-title":"Statistical Science"},{"key":"10628_CR10","unstructured":"Ray, P., Bhattacharya, A.: Signal adaptive variable selector for the horseshoe prior arXiv:1810.09004"},{"key":"10628_CR11","doi-asserted-by":"publisher","first-page":"367","DOI":"10.1111\/1467-9868.00391","volume":"65","author":"A Azzalini","year":"2003","unstructured":"Azzalini, A., Capitanio, A.: Distributions generated by perturbation of symmetry with emphasis on a multivariate skew $$t$$-distribution. Journal of the Royal Statistical Society: Series B 65, 367\u2013389 (2003)","journal-title":"Journal of the Royal Statistical Society: Series B"},{"key":"10628_CR12","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1080\/01621459.1999.10474163","volume":"94","author":"SM Berry","year":"1999","unstructured":"Berry, S.M., Reese, C.S., Larkey, P.D.: Bridging different eras in sports. Journal of the American Statistical Association 94, 661\u2013676 (1999)","journal-title":"Journal of the American Statistical Association"},{"key":"10628_CR13","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1515\/jqas-2021-0112","volume":"18","author":"JE Griffin","year":"2022","unstructured":"Griffin, J.E., Hinoveanu, L.C., Hopker, J.G.: Bayesian modelling of elite sporting performance with large databases. Journal of Quantitative Analysis in Sports 18, 253\u2013268 (2022)","journal-title":"Journal of Quantitative Analysis in Sports"},{"key":"10628_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","volume":"39","author":"AP Dempster","year":"1977","unstructured":"Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society, Series B 39, 1\u201338 (1977)","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"10628_CR15","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1111\/1467-9868.00082","volume":"59","author":"X-L Meng","year":"1997","unstructured":"Meng, X.-L., Dyk, D.: The EM algorithm - an old folk-song sung to a fast new tune. Journal of the Royal Statistical Society, Series B 59, 511\u2013567 (1997)","journal-title":"Journal of the Royal Statistical Society, Series B"},{"key":"10628_CR16","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","volume":"112","author":"DM Blei","year":"2017","unstructured":"Blei, D.M., Kucukelbir, A., McAuliffe, J.D.: Variational Inference: A Review for Statisticians. Journal of the American Statistical Association 112, 859\u2013877 (2017)","journal-title":"Journal of the American Statistical Association"},{"key":"10628_CR17","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1080\/01621459.1994.10476894","volume":"89","author":"D Madigan","year":"1994","unstructured":"Madigan, D., Raftery, A.E.: Model selection and accounting for model uncertainty in graphical models using Occam\u2019s window. Journal of the American Statistical Association 89, 1535\u20131546 (1994)","journal-title":"Journal of the American Statistical Association"},{"key":"10628_CR18","doi-asserted-by":"publisher","first-page":"56","DOI":"10.1186\/s12874-024-02164-y","volume":"24","author":"MM Ferede","year":"2024","unstructured":"Ferede, M.M., Dagne, G.A., Mwalili, S.M., Bilchut, W.H., Engida, H.A., Karanja, S.M.: Flexible Bayesian semiparametric mixed-effects model for skewed longitudinal data. BMC Medical Research Methodology 24, 56 (2024)","journal-title":"BMC Medical Research Methodology"},{"key":"10628_CR19","doi-asserted-by":"publisher","first-page":"2455","DOI":"10.1007\/s10694-023-01436-1","volume":"59","author":"M Gong","year":"2023","unstructured":"Gong, M., Mao, Z., Zhang, D., Ren, J., Zuo, S.: Study on Bayesian Skew-Normal Linear Mixed Model and Its Application in Fire Insurance. Fire Technology 59, 2455\u20132480 (2023)","journal-title":"Fire Technology"},{"key":"10628_CR20","doi-asserted-by":"crossref","unstructured":"Wand, M.P., Ormerod, J.T., Padoan, S.A., Fr\u00fchwirth, R.: Mean field Variational Bayes for elaborate distributions. Bayesian Analysis 6, 847\u2013900 (2011)","DOI":"10.1214\/11-BA631"},{"key":"10628_CR21","doi-asserted-by":"publisher","first-page":"377","DOI":"10.1016\/j.jcp.2015.07.062","volume":"301","author":"N Guha","year":"2015","unstructured":"Guha, N., Wu, X., Efendiev, Y., Jin, B., Mallick, B.K.: A variational Bayesian approach for inverse problems with skew-t error distributions. Journal of Computational Physics 301, 377\u2013393 (2015)","journal-title":"Journal of Computational Physics"},{"key":"10628_CR22","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1214\/009053604000000238","volume":"32","author":"MM Barbieri","year":"2004","unstructured":"Barbieri, M.M., Berger, J.O.: Optimal predictive model selection. Annals of Statistics 32, 870\u2013897 (2004)","journal-title":"Annals of Statistics"}],"container-title":["Statistics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10628-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11222-025-10628-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11222-025-10628-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,6]],"date-time":"2025-09-06T18:36:06Z","timestamp":1757183766000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11222-025-10628-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,9]]},"references-count":22,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2025,10]]}},"alternative-id":["10628"],"URL":"https:\/\/doi.org\/10.1007\/s11222-025-10628-4","relation":{},"ISSN":["0960-3174","1573-1375"],"issn-type":[{"value":"0960-3174","type":"print"},{"value":"1573-1375","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,9]]},"assertion":[{"value":"14 August 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"122"}}