{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,10,6]],"date-time":"2024-10-06T03:10:31Z","timestamp":1728184231797},"reference-count":41,"publisher":"SAGE Publications","issue":"10","license":[{"start":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T00:00:00Z","timestamp":1596067200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"funder":[{"DOI":"10.13039\/501100004260","name":"renmin university of china","doi-asserted-by":"publisher","award":["16XNH102"],"id":[{"id":"10.13039\/501100004260","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"fundamental research funds for the central universities","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["SIMULATION"],"published-print":{"date-parts":[[2020,10]]},"abstract":" Missing data is almost inevitable for various reasons in many applications. For hierarchical latent variable models, there usually exist two kinds of missing data problems. One is manifest variables with incomplete observations, the other is latent variables which cannot be observed directly. Missing data in manifest variables can be handled by different methods. For latent variables, there exist several kinds of partial least square (PLS) algorithms which have been widely used to estimate the value of latent variables. In this paper, we not only combine traditional linear regression type PLS algorithms with missing data handling methods, but also introduce quantile regression to improve the performances of PLS algorithms when the relationships among manifest and latent variables are not fixed according to the explored quantile of interest. Thus, we can get the overall view of variables\u2019 relationships at different levels. The main challenges lie in how to introduce quantile regression in PLS algorithms correctly and how well the PLS algorithms perform when missing manifest variables occur. By simulation studies, we compare all the PLS algorithms with missing data handling methods in different settings, and finally build a business sophistication hierarchical latent variable model based on real data. <\/jats:p>","DOI":"10.1177\/0037549720944467","type":"journal-article","created":{"date-parts":[[2020,7,30]],"date-time":"2020-07-30T09:51:00Z","timestamp":1596102660000},"page":"825-839","update-policy":"http:\/\/dx.doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Comparison of partial least square algorithms in hierarchical latent variable model with missing data"],"prefix":"10.1177","volume":"96","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-1143-9601","authenticated-orcid":false,"given":"Hao","family":"Cheng","sequence":"first","affiliation":[{"name":"National Academy of Innovation Strategy, China Association for Science and Technology, China"},{"name":"School of Statistics, Renmin University of China, China"},{"name":"Department of Biostatistics, Columbia University, USA"},{"name":"Needham Research Institute, Cambridge University, UK"}]}],"member":"179","published-online":{"date-parts":[[2020,7,30]]},"reference":[{"key":"bibr1-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1007\/s11336-019-09679-0"},{"key":"bibr2-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1186\/s12913-019-4094-1"},{"key":"bibr3-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1021\/acs.iecr.9b03262"},{"key":"bibr4-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1097\/MD.0000000000009916"},{"key":"bibr5-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1016\/j.lrp.2012.10.001"},{"key":"bibr6-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1002\/9781118619179"},{"key":"bibr7-0037549720944467","doi-asserted-by":"publisher","DOI":"10.2307\/2532903"},{"volume-title":"Statistical analysis with missing data","year":"1987","author":"Little RJA","key":"bibr8-0037549720944467"},{"key":"bibr9-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/ass007"},{"key":"bibr10-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/asq073"},{"key":"bibr11-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1007\/s00180-018-0813-z"},{"key":"bibr12-0037549720944467","first-page":"26","volume":"7","author":"Cheng H","year":"2019","journal-title":"Statistics and Information Forum"},{"key":"bibr13-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-52512-4"},{"key":"bibr14-0037549720944467","doi-asserted-by":"publisher","DOI":"10.2307\/20650284"},{"key":"bibr15-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1016\/S0003-2670(01)85039-X"},{"volume-title":"A primer on partial least squares structural equation modeling (PLS-SEM)","year":"2014","author":"Hair JF","key":"bibr16-0037549720944467"},{"key":"bibr17-0037549720944467","first-page":"1","volume-title":"Systems under indirect observations: part II","author":"Wold H","year":"1982"},{"key":"bibr18-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1080\/10485250903009037"},{"key":"bibr19-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1080\/02664769922322"},{"key":"bibr20-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-32827-8"},{"key":"bibr21-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1177\/002224378201900406"},{"key":"bibr22-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1016\/S0169-7439(01)00163-0"},{"key":"bibr23-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1108\/S1474-7979(2009)0000020014"},{"key":"bibr24-0037549720944467","doi-asserted-by":"publisher","DOI":"10.4337\/9781781001042.00023"},{"volume-title":"PLS path modeling with R","year":"2013","author":"Sanchez G","key":"bibr25-0037549720944467"},{"key":"bibr26-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32903-6_14"},{"issue":"2","key":"bibr27-0037549720944467","first-page":"5","volume":"47","author":"Tenenhaus M","year":"1999","journal-title":"Revue de Statistique Applique"},{"key":"bibr28-0037549720944467","doi-asserted-by":"publisher","DOI":"10.1016\/j.csda.2004.03.005"},{"key":"bibr29-0037549720944467","unstructured":"Chatelin YM, Vinzi Esposito V, Tenenhaus M. 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