{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T07:58:09Z","timestamp":1772783889244,"version":"3.50.1"},"reference-count":40,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T00:00:00Z","timestamp":1709856000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Shandong Provincial Natural Foundation of China","award":["ZR2021QA053"],"award-info":[{"award-number":["ZR2021QA053"]}]},{"name":"Shandong Provincial Natural Foundation of China","award":["ZR2021QA044"],"award-info":[{"award-number":["ZR2021QA044"]}]},{"name":"Shandong Provincial Natural Foundation of China","award":["(12101346"],"award-info":[{"award-number":["(12101346"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZR2021QA053"],"award-info":[{"award-number":["ZR2021QA053"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["ZR2021QA044"],"award-info":[{"award-number":["ZR2021QA044"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["(12101346"],"award-info":[{"award-number":["(12101346"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>Supersaturated designs (SSDs) refer to those designs in which the run size is much smaller than the main effects to be estimated. They are commonly used to identify a few, but critical, active factors from a large set of potentially active ones, keeping the cost as low as possible. In this regard, the development of new construction and analysis methods has recently seen a rapid increase. In this paper, we provide some methods to construct equi- and mixed-level E(f\u00a0NOD) optimal SSDs with a large number of inert factors using the substitution method. The proposed methods are easy to implement, and many new SSDs can then be constructed from them. We also study a variable selection method based on the screening-selection network (SSnet) method for regression problems. A real example is analyzed to illustrate that it is able to effectively identify active factors. Eight different analysis methods are used to analyze the data generated from the proposed designs. Three scenarios with different setups of parameters are designed, and the performances of each method are illustrated by extensive simulation studies. Among all these methods, SSnet produced the most satisfactory results according to power.<\/jats:p>","DOI":"10.3390\/axioms13030179","type":"journal-article","created":{"date-parts":[[2024,3,8]],"date-time":"2024-03-08T03:52:11Z","timestamp":1709869931000},"page":"179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Construction and Analysis for the Optimal Supersaturated Designs with a Large Number of Inert Factors"],"prefix":"10.3390","volume":"13","author":[{"given":"Xiaoqing","family":"Hong","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weiping","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0930-8357","authenticated-orcid":false,"given":"Xiao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Min","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,3,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1080\/00401706.1959.10489853","article-title":"Random balance experimentation","volume":"1","author":"Satterthwaite","year":"1959","journal-title":"Technometrics"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1080\/00401706.1962.10490035","article-title":"Some systematic supersaturated designs","volume":"4","author":"Booth","year":"1962","journal-title":"Technometrics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1080\/00401706.1993.10484990","article-title":"A new class of supersaturated designs","volume":"35","author":"Lin","year":"1993","journal-title":"Technometrics"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1093\/biomet\/80.3.661","article-title":"Construction of supersaturated designs through partially aliased interactions","volume":"80","author":"Wu","year":"1993","journal-title":"Biometrika"},{"key":"ref_5","unstructured":"Fang, K.T., Lin, D.K.J., and Liu, M.Q. (2000). Optimal Mixed-Level Supersaturated Design and Computer Experiment, Hong Kong Baptist University. Technical Report MATH-286."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1007\/s001840300266","article-title":"Optimal mixed-level supersaturated design","volume":"58","author":"Fang","year":"2003","journal-title":"Metrika"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s001840100173","article-title":"Construction of mixed-level supersaturated design","volume":"56","author":"Yamada","year":"2002","journal-title":"Metrika"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1007\/s10255-022-1113-5","article-title":"A Note on Supersaturated Design","volume":"38","author":"Zou","year":"2022","journal-title":"Acta Math. Appl. Sin. Engl. Ser."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2805","DOI":"10.1016\/j.jspi.2004.11.002","article-title":"On multi-level supersaturated designs","volume":"136","author":"Georgiou","year":"2006","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_10","first-page":"1705","article-title":"Construction of mixed-level supersaturated designs by the substitution method","volume":"19","author":"Liu","year":"2009","journal-title":"Stat. Sin."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1310","DOI":"10.1214\/11-AOS877","article-title":"On construction of optimal mixed-level supersaturated designs","volume":"39","author":"Sun","year":"2011","journal-title":"Ann. Stat."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.jspi.2012.09.014","article-title":"Supersaturated designs: A review of their construction and analysis","volume":"144","author":"Georgiou","year":"2014","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1979","DOI":"10.1080\/03610918.2018.1429620","article-title":"Sure independence screening for analyzing supersaturated designs","volume":"48","author":"Drosou","year":"2018","journal-title":"Commun. Stat.-Simul. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/00401706.2019.1654926","article-title":"Construction, properties, and analysis of group-orthogonal supersaturated designs","volume":"62","author":"Jones","year":"2020","journal-title":"Technometrics"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1007\/s00184-020-00792-0","article-title":"Construction of mixed-level supersaturated split-plot designs","volume":"84","author":"Chatterjee","year":"2021","journal-title":"Metrika"},{"key":"ref_16","first-page":"46","article-title":"The development of a method for constructing supersaturated design and nearly orthogonal design with mixed-level orthogonal design","volume":"10","author":"Khurana","year":"2021","journal-title":"Curr. Top. Math. Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Daraz, U., Chen, E., and Tang, Y. (2022). Supersaturated designs with less \u03b2-aberration. Commun. Stat.-Theory Methods.","DOI":"10.1080\/03610926.2022.2150828"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2565","DOI":"10.1080\/03610926.2020.1777309","article-title":"Construction of optimal supersaturated designs via generalized Hadamard matrices","volume":"51","author":"Li","year":"2022","journal-title":"Commun. Stat.-Theory Methods Taylor Fr. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","article-title":"Regression Shrinkage and Selection via the LASSO","volume":"58","author":"Tibshirani","year":"1996","journal-title":"J. R. Stat. Soc. Ser. B-Methodol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","article-title":"Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties","volume":"96","author":"Fan","year":"2001","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/S0167-7152(02)00140-2","article-title":"Data analysis in supersaturated designs","volume":"59","author":"Li","year":"2002","journal-title":"Stat. Probab. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1418","DOI":"10.1198\/016214506000000735","article-title":"The Adaptive Lasso and Its Oracle Properties","volume":"101","author":"Zou","year":"2006","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1111\/j.1467-9868.2008.00674.x","article-title":"Sure Independence Screening for Ultrahigh Dimensional Feature Space","volume":"70","author":"Fan","year":"2008","journal-title":"J. R. Stat. Soc. Ser. B Stat. Methodol."},{"key":"ref_24","first-page":"2313","article-title":"The Dantzig selector: Statistical estimation when p is much larger than n","volume":"35","author":"Candes","year":"2007","journal-title":"Ann. Stat."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"2362","DOI":"10.1016\/j.jspi.2008.10.023","article-title":"Analysis of supersaturated designs via the Dantzig selector","volume":"139","author":"Phoa","year":"2009","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.csda.2014.02.023","article-title":"Screening active factors in supersaturated designs","volume":"77","author":"Das","year":"2014","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1214\/09-AOS729","article-title":"Nearly unbiased variable selection under minimax concave penalty","volume":"38","author":"Zhang","year":"2010","journal-title":"Ann. Stat."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1080\/00224065.2018.1541389","article-title":"A new variable selection method based on SVM for analyzing supersaturated designs","volume":"51","author":"Drosou","year":"2019","journal-title":"J. Qual. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"244","DOI":"10.1080\/00224065.2017.11917993","article-title":"Using definitive screening designs to identify active firstand second-order factor effects","volume":"49","author":"Errore","year":"2017","journal-title":"J. Qual. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"60","DOI":"10.17929\/tqs.7.60","article-title":"Discussion on supersaturated design and its data analysis method in computer experiments","volume":"7","author":"Ueda","year":"2022","journal-title":"Total Qual. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1111\/sjos.12546","article-title":"Improving Lasso for model selection and prediction","volume":"49","author":"Pokarowski","year":"2022","journal-title":"Scand. J. Stat."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"508","DOI":"10.1214\/aoms\/1177729331","article-title":"Orthogonal arrays of strength two and three","volume":"23","author":"Bose","year":"1952","journal-title":"Ann. Math. Stat."},{"key":"ref_33","first-page":"2362","article-title":"Orthogonal Arrays: Theory and Applications","volume":"139","author":"Hedayat","year":"1999","journal-title":"Springer Ser. Stat. Springer-Verlag. J. Stat. Plan. Inference"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/S0012-365X(03)00269-3","article-title":"Combinatorial constructions for optimal supersaturated designs","volume":"279","author":"Fang","year":"2004","journal-title":"Discret. Math."},{"key":"ref_35","first-page":"65","article-title":"Designed experiments","volume":"100","author":"Williams","year":"1968","journal-title":"Rubber Age"},{"key":"ref_36","first-page":"135","article-title":"Some Risks in the Construction and Analysis of Supersaturated Designs","volume":"41","author":"Abraham","year":"1999","journal-title":"Ann. Stat."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1198\/004017002753398326","article-title":"A Two-Stage Bayesian Model Selection Strategy for Supersaturated Designs","volume":"44","author":"Beattie","year":"2002","journal-title":"Technometrics"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"249","DOI":"10.6339\/JDS.2003.01(3).134","article-title":"Analysis Methods for Supersaturated Design: Some Comparisons","volume":"1","author":"Li","year":"2003","journal-title":"J. Data Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1080\/00401706.1986.10488094","article-title":"Dispersion effects from fractional designs","volume":"28","author":"Box","year":"1986","journal-title":"Technometrics"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3158","DOI":"10.1016\/j.csda.2010.02.017","article-title":"A comparison of design and model selection methods for supersaturated experiments","volume":"54","author":"Marley","year":"2010","journal-title":"Comput. Stat. Data Anal."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/179\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:10:45Z","timestamp":1760105445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/13\/3\/179"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3,8]]},"references-count":40,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2024,3]]}},"alternative-id":["axioms13030179"],"URL":"https:\/\/doi.org\/10.3390\/axioms13030179","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3,8]]}}}