{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T01:07:09Z","timestamp":1779930429454,"version":"3.53.1"},"reference-count":57,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T00:00:00Z","timestamp":1777593600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100024370","name":"Ministero dell'Istruzione dell'Universita e della Ricerca","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100024370","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Computational Statistics &amp; Data Analysis"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.csda.2026.108402","type":"journal-article","created":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:59:49Z","timestamp":1777647589000},"page":"108402","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["A penalized maximum likelihood approach to deal with latent state separation in hidden Markov models with covariates and lagged responses"],"prefix":"10.1016","volume":"222","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8156-470X","authenticated-orcid":false,"given":"Luca","family":"Brusa","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fulvia","family":"Pennoni","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Francesco","family":"Bartolucci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Romina","family":"Peruilh Bagolini","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.csda.2026.108402_bib0001","series-title":"Categorical Data Analysis, 2nd Edition","author":"Agresti","year":"2002"},{"key":"10.1016\/j.csda.2026.108402_bib0002","first-page":"1","article-title":"Comparison of predictor approaches for longitudinal binary outcomes: application to anesthesiology data","volume":"2","author":"Aktas","year":"2014","journal-title":"PeerJ"},{"key":"10.1016\/j.csda.2026.108402_bib0003","doi-asserted-by":"crossref","first-page":"6133","DOI":"10.1080\/03610926.2014.957855","article-title":"Penalized maximum likelihood estimation for Gaussian hidden Markov models","volume":"45","author":"Alexandrovich","year":"2016","journal-title":"Commun. Stat. \u2013 Theory Methods"},{"key":"10.1016\/j.csda.2026.108402_bib0004","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1080\/10618600.2016.1172018","article-title":"Composite likelihood inference in a discrete latent variable model for two-way \u201cclustering-by-segmentation\u201d problems","volume":"26","author":"Bartolucci","year":"2017","journal-title":"J. Comput. Graph. Stat."},{"key":"10.1016\/j.csda.2026.108402_bib0005","doi-asserted-by":"crossref","first-page":"816","DOI":"10.1198\/jasa.2009.0107","article-title":"A multivariate extension of the dynamic logit model for longitudinal data based on a latent Markov heterogeneity structure","volume":"104","author":"Bartolucci","year":"2009","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108402_bib0006","series-title":"Latent Markov Models for Longitudinal Data","author":"Bartolucci","year":"2013"},{"key":"10.1016\/j.csda.2026.108402_bib0007","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1007\/s11749-014-0381-7","article-title":"Latent Markov models: a review of a general framework for the analysis of longitudinal data with covariates","volume":"23","author":"Bartolucci","year":"2014","journal-title":"Test"},{"key":"10.1016\/j.csda.2026.108402_bib0008","doi-asserted-by":"crossref","first-page":"568","DOI":"10.1111\/j.1541-0420.2006.00702.x","article-title":"A class of latent Markov models for capture\u2013recapture data allowing for time, heterogeneity, and behavior effects","volume":"63","author":"Bartolucci","year":"2007","journal-title":"Biometrics"},{"key":"10.1016\/j.csda.2026.108402_bib0009","first-page":"1234","article-title":"Cross-validation: what does it estimate and how well does it do it?","volume":"24","author":"Bates","year":"2023","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.csda.2026.108402_bib0010","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1214\/aoms\/1177699147","article-title":"Statistical inference for probabilistic functions of finite state Markov chains","volume":"37","author":"Baum","year":"1966","journal-title":"Ann. Math. Stat."},{"key":"10.1016\/j.csda.2026.108402_bib0011","series-title":"Classification and Regression Trees","author":"Breiman","year":"1984"},{"key":"10.1016\/j.csda.2026.108402_bib0012","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1348\/000711008X320134","article-title":"Latent variable models for multivariate longitudinal ordinal responses","volume":"62","author":"Cagnone","year":"2009","journal-title":"Br. J. Math. Stat. Psychol."},{"key":"10.1016\/j.csda.2026.108402_bib0013","doi-asserted-by":"crossref","first-page":"906","DOI":"10.1097\/00000542-199206000-00006","article-title":"Incidence and risk factors for side effects of spinal anesthesia","volume":"76","author":"Carpenter","year":"1992","journal-title":"Anesthesiology"},{"key":"10.1016\/j.csda.2026.108402_bib0014","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/0167-9473(92)90042-E","article-title":"A classification EM algorithm for clustering and two stochastic versions","volume":"14","author":"Celeux","year":"1992","journal-title":"Comput. Stat. Data Anal."},{"key":"10.1016\/j.csda.2026.108402_bib0015","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.rmal.2023.100044","article-title":"Dealing with complete separation and quasi-complete separation in logistic regression for linguistic data","volume":"2","author":"Clark","year":"2023","journal-title":"Res. Methods Appl. Linguist."},{"key":"10.1016\/j.csda.2026.108402_bib0016","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum likelihood from incomplete data via the EM algorithm (with discussion)","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Stat. Soc. B"},{"key":"10.1016\/j.csda.2026.108402_bib0017","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1002\/bimj.201700007","article-title":"Penalized estimation in latent Markov models, with application to monitoring serum calcium levels in end-stage kidney insufficiency","volume":"59","author":"Farcomeni","year":"2017","journal-title":"Biom. J."},{"key":"10.1016\/j.csda.2026.108402_bib0018","series-title":"Applied Longitudinal Analysis","author":"Fitzmaurice","year":"2012"},{"key":"10.1016\/j.csda.2026.108402_bib0019","doi-asserted-by":"crossref","first-page":"255","DOI":"10.2307\/2334515","article-title":"Nonparametric roughness penalties for probability densities","volume":"58","author":"Good","year":"1971","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2026.108402_bib0020","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1093\/biomet\/61.2.215","article-title":"Exploratory latent structure analysis using both identifiable and unidentifiable models","volume":"61","author":"Goodman","year":"1974","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2026.108402_bib0021","doi-asserted-by":"crossref","first-page":"1521","DOI":"10.1213\/00000539-200206000-00027","article-title":"The incidence and risk factors for hypotension after spinal anesthesia induction: an analysis with automated data collection","volume":"94","author":"Hartmann","year":"2002","journal-title":"Anesth. Analg."},{"key":"10.1016\/j.csda.2026.108402_bib0022","series-title":"The Elements of Statistical Learning: Data Mining, Inference, and Prediction, 2nd Edition","author":"Hastie","year":"2009"},{"key":"10.1016\/j.csda.2026.108402_bib0023","series-title":"Analysis of Panel Data, 2nd Edition","author":"Hsiao","year":"2003"},{"key":"10.1016\/j.csda.2026.108402_bib0024","doi-asserted-by":"crossref","first-page":"1469","DOI":"10.1080\/01621459.2013.836973","article-title":"Hidden Markov models with applications in cell adhesion experiments","volume":"108","author":"Hung","year":"2013","journal-title":"J. Am. Stat. Assoc."},{"key":"10.1016\/j.csda.2026.108402_bib0025","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1111\/j.1399-6576.2010.02239.x","article-title":"Definitions of hypotension after spinal anaesthesia for caesarean section: literature search and application to parturients","volume":"54","author":"Kl\u00f6hr","year":"2010","journal-title":"Acta Anaesthesiol. Scand."},{"key":"10.1016\/j.csda.2026.108402_bib0026","series-title":"Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI)","first-page":"1137","article-title":"A study of cross-validation and bootstrap for accuracy estimation and model selection","volume":"Vol. 2","author":"Kohavi","year":"1995"},{"key":"10.1016\/j.csda.2026.108402_bib0027","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1758-2946-6-10","article-title":"Cross-validation pitfalls when selecting and assessing regression and classification models","volume":"6","author":"Krstajic","year":"2014","journal-title":"J. Cheminformatics"},{"key":"10.1016\/j.csda.2026.108402_bib0028","doi-asserted-by":"crossref","first-page":"520","DOI":"10.1111\/biom.12282","article-title":"Nonparametric inference in hidden Markov models using P-splines","volume":"71","author":"Langrock","year":"2015","journal-title":"Biometrics"},{"key":"10.1016\/j.csda.2026.108402_bib0029","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1093\/biomet\/73.1.13","article-title":"Longitudinal data analysis using generalized linear models","volume":"73","author":"Liang","year":"1986","journal-title":"Biometrika"},{"key":"10.1016\/j.csda.2026.108402_bib0030","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.cmpb.2008.06.013","article-title":"Predicting hypotensive episodes during spinal anesthesia with the application of artificial neural networks","volume":"92","author":"Lin","year":"2008","journal-title":"Comput. Methods Programs Biomed."},{"key":"10.1016\/j.csda.2026.108402_bib0031","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.jmva.2022.105061","article-title":"Order selection for regression-based hidden Markov model","volume":"192","author":"Lin","year":"2022","journal-title":"J. Multivar. Anal."},{"key":"10.1016\/j.csda.2026.108402_bib0032","doi-asserted-by":"crossref","first-page":"864","DOI":"10.1093\/aje\/kwx299","article-title":"Separation in logistic regression: causes, consequences, and control","volume":"187","author":"Mansournia","year":"2017","journal-title":"Am. J. Epidemiol."},{"key":"10.1016\/j.csda.2026.108402_bib0033","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.csda.2016.05.024","article-title":"Model-based time-varying clustering of multivariate longitudinal data with covariates and outliers","volume":"113","author":"Maruotti","year":"2017","journal-title":"Comput. Stat. Data Anal."},{"key":"10.1016\/j.csda.2026.108402_bib0034","series-title":"Generalized Linear Models, 2nd Edition","author":"McCullagh","year":"1989"},{"key":"10.1016\/j.csda.2026.108402_bib0035","series-title":"Generalized Linear Mixed Models","author":"McCulloch","year":"2008"},{"key":"10.1016\/j.csda.2026.108402_bib0036","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF02296300","article-title":"Efficient estimation and local identification in latent class analysis","volume":"21","author":"McHugh","year":"1956","journal-title":"Psychometrika"},{"key":"10.1016\/j.csda.2026.108402_bib0037","series-title":"Finite Mixture Models","author":"McLachlan","year":"2000"},{"key":"10.1016\/j.csda.2026.108402_bib0038","doi-asserted-by":"crossref","first-page":"1429","DOI":"10.1007\/s11831-020-09422-4","article-title":"A systematic review of hidden Markov models and their applications","volume":"28","author":"Mor","year":"2021","journal-title":"Arch. Comput. Methods Eng."},{"key":"10.1016\/j.csda.2026.108402_bib0039","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1111\/1467-9868.00188","article-title":"Direct calculation of the information matrix via the EM algorithm","volume":"61","author":"Oakes","year":"1999","journal-title":"J. R. Stat. Soc. B"},{"key":"10.1016\/j.csda.2026.108402_bib0040","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1177\/1471082X211008014","article-title":"A regularized hidden Markov model for analyzing the \u2018hot shoe\u2019 in football","volume":"22","author":"\u00d6tting","year":"2022","journal-title":"Stat. Model."},{"key":"10.1016\/j.csda.2026.108402_bib0041","first-page":"1","article-title":"Spinal anaesthesia using hypobaric drugs: a review of current evidence","volume":"16","author":"Paliwal","year":"2024","journal-title":"Cureus"},{"key":"10.1016\/j.csda.2026.108402_bib0042","series-title":"Issues on the Estimation of Latent Variable and Latent Class Models","author":"Pennoni","year":"2014"},{"key":"10.1016\/j.csda.2026.108402_bib0043","doi-asserted-by":"crossref","first-page":"74","DOI":"10.32614\/RJ-2024-036","article-title":"LMest: An R package for estimating generalized latent Markov models","volume":"16","author":"Pennoni","year":"2025","journal-title":"R J."},{"key":"10.1016\/j.csda.2026.108402_bib0044","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijoa.2024.104208","article-title":"Total spinal anaesthesia following obstetric neuraxial blockade: a narrative review","volume":"59","author":"Radwan","year":"2024","journal-title":"Int. J. Obstet. Anesth."},{"key":"10.1016\/j.csda.2026.108402_bib0045","doi-asserted-by":"crossref","first-page":"577","DOI":"10.2307\/1913267","article-title":"Identification in parametric models","volume":"39","author":"Rothenberg","year":"1971","journal-title":"Econometrica"},{"key":"10.1016\/j.csda.2026.108402_bib0046","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1097\/00000542-199611000-00004","article-title":"Detection of intraoperative incidents by electronic scanning of computerized anesthesia records: comparison with voluntary reporting","volume":"85","author":"Sanborn","year":"1996","journal-title":"Anesthesiology"},{"key":"10.1016\/j.csda.2026.108402_bib0047","series-title":"Medical Applications of Finite Mixture Models","author":"Schlattmann","year":"2009"},{"key":"10.1016\/j.csda.2026.108402_bib0048","series-title":"Graphical Representation of Multivariate Data","first-page":"169","article-title":"Multivariate density estimation by discrete maximum penalized likelihood methods","author":"Scott","year":"1978"},{"key":"10.1016\/j.csda.2026.108402_bib0049","first-page":"111","article-title":"Prevention of hypotension during spinal anesthesia: a comparison of intravascular administration of hetastarch versus lactated ringer\u2019s solution","volume":"84","author":"Sharma","year":"1997","journal-title":"Anesth. Analg."},{"key":"10.1016\/j.csda.2026.108402_bib0050","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1214\/aos\/1176345872","article-title":"On the estimation of a probability density function by the maximum penalized likelihood method","volume":"10","author":"Silverman","year":"1982","journal-title":"Ann. Stat."},{"key":"10.1016\/j.csda.2026.108402_bib0051","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1023\/A:1008940618127","article-title":"Model selection for probabilistic clustering using cross-validated likelihood","volume":"9","author":"Smyth","year":"2000","journal-title":"Stat. Comput."},{"key":"10.1016\/j.csda.2026.108402_bib0052","first-page":"181","article-title":"Incidence and risk factors of hypotension and bradycardia after spinal anesthesia for cesarean section","volume":"91","author":"Somboonviboon","year":"2008","journal-title":"J. Med. Assoc. Thail."},{"key":"10.1016\/j.csda.2026.108402_bib0053","series-title":"The C++ Programming Language, 4th Edition","author":"Stroustrup","year":"2013"},{"key":"10.1016\/j.csda.2026.108402_bib0054","unstructured":"R Core Team, 2025. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Vienna, Austria. https:\/\/www.R-project.org\/."},{"key":"10.1016\/j.csda.2026.108402_bib0055","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. B"},{"key":"10.1016\/j.csda.2026.108402_bib0056","series-title":"Mixture and Hidden Markov Models with R","author":"Visser","year":"2022"},{"key":"10.1016\/j.csda.2026.108402_bib0057","first-page":"10","article-title":"Hidden Markov models and the Baum-Welch algorithm","volume":"50","author":"Welch","year":"2003","journal-title":"IEEE Inform. Theory Soc. Newsl."}],"container-title":["Computational Statistics &amp; Data Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S016794732600071X?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S016794732600071X?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,5,28]],"date-time":"2026-05-28T00:46:17Z","timestamp":1779929177000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S016794732600071X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":57,"alternative-id":["S016794732600071X"],"URL":"https:\/\/doi.org\/10.1016\/j.csda.2026.108402","relation":{},"ISSN":["0167-9473"],"issn-type":[{"value":"0167-9473","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"A penalized maximum likelihood approach to deal with latent state separation in hidden Markov models with covariates and lagged responses","name":"articletitle","label":"Article Title"},{"value":"Computational Statistics & Data Analysis","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.csda.2026.108402","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Authors. Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"108402"}}