{"id":"https://openalex.org/W7160194643","doi":"https://doi.org/10.1016/j.csda.2026.108402","title":"A penalized maximum likelihood approach to deal with latent state separation in hidden Markov models with covariates and lagged responses","display_name":"A penalized maximum likelihood approach to deal with latent state separation in hidden Markov models with covariates and lagged responses","publication_year":2026,"publication_date":"2026-05-01","ids":{"openalex":"https://openalex.org/W7160194643","doi":"https://doi.org/10.1016/j.csda.2026.108402"},"language":"en","primary_location":{"id":"doi:10.1016/j.csda.2026.108402","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.csda.2026.108402","pdf_url":null,"source":{"id":"https://openalex.org/S132362803","display_name":"Computational Statistics & Data Analysis","issn_l":"0167-9473","issn":["0167-9473","1872-7352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics &amp; Data Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.csda.2026.108402","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001199768","display_name":"Luca Brusa","orcid":"https://orcid.org/0000-0002-8156-470X"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Luca Brusa","raw_affiliation_strings":["Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, Milan, 20126, Italy"],"raw_orcid":"https://orcid.org/0000-0002-8156-470X","affiliations":[{"raw_affiliation_string":"Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, Milan, 20126, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021943787","display_name":"Fulvia Pennoni","orcid":"https://orcid.org/0000-0002-6331-7211"},"institutions":[{"id":"https://openalex.org/I66752286","display_name":"University of Milano-Bicocca","ror":"https://ror.org/01ynf4891","country_code":"IT","type":"education","lineage":["https://openalex.org/I66752286"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Fulvia Pennoni","raw_affiliation_strings":["Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, Milan, 20126, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics and Quantitative Methods, University of Milano-Bicocca, Via Bicocca degli Arcimboldi 8, Milan, 20126, Italy","institution_ids":["https://openalex.org/I66752286"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054448743","display_name":"Francesco Bartolucci","orcid":"https://orcid.org/0000-0001-7057-1421"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]},{"id":"https://openalex.org/I4210163778","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Perugia","ror":"https://ror.org/05478fx36","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210163778"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Francesco Bartolucci","raw_affiliation_strings":["Department of Economics, University of Perugia, Via Alessandro Pascoli 20, Perugia, 06123, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, University of Perugia, Via Alessandro Pascoli 20, Perugia, 06123, Italy","institution_ids":["https://openalex.org/I27483092","https://openalex.org/I4210163778"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5116475612","display_name":"Romina Peruilh Bagolini","orcid":null},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]},{"id":"https://openalex.org/I4210163778","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Perugia","ror":"https://ror.org/05478fx36","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210163778"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Romina Peruilh Bagolini","raw_affiliation_strings":["Department of Economics, University of Perugia, Via Alessandro Pascoli 20, Perugia, 06123, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics, University of Perugia, Via Alessandro Pascoli 20, Perugia, 06123, Italy","institution_ids":["https://openalex.org/I27483092","https://openalex.org/I4210163778"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001199768"],"corresponding_institution_ids":["https://openalex.org/I66752286"],"apc_list":{"value":3340,"currency":"USD","value_usd":3340},"apc_paid":{"value":3340,"currency":"USD","value_usd":3340},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.63516944,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"222","issue":null,"first_page":"108402","last_page":"108402"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.41339999437332153,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.41339999437332153,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10711","display_name":"Target Tracking and Data Fusion in Sensor Networks","score":0.07490000128746033,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12814","display_name":"Gaussian Processes and Bayesian Inference","score":0.05869999900460243,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/covariate","display_name":"Covariate","score":0.6804999709129333},{"id":"https://openalex.org/keywords/hidden-markov-model","display_name":"Hidden Markov model","score":0.5784000158309937},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.5612000226974487},{"id":"https://openalex.org/keywords/separation","display_name":"Separation (statistics)","score":0.521399974822998},{"id":"https://openalex.org/keywords/hidden-semi-markov-model","display_name":"Hidden semi-Markov model","score":0.48089998960494995},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.45669999718666077},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.4083000123500824},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.4020000100135803},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.3707999885082245}],"concepts":[{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.6804999709129333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6693000197410583},{"id":"https://openalex.org/C23224414","wikidata":"https://www.wikidata.org/wiki/Q176769","display_name":"Hidden Markov model","level":2,"score":0.5784000158309937},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.5612000226974487},{"id":"https://openalex.org/C2776061190","wikidata":"https://www.wikidata.org/wiki/Q7451805","display_name":"Separation (statistics)","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5045999884605408},{"id":"https://openalex.org/C64939953","wikidata":"https://www.wikidata.org/wiki/Q3859882","display_name":"Hidden semi-Markov model","level":5,"score":0.48089998960494995},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.45669999718666077},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.41350001096725464},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.4083000123500824},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.4020000100135803},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.3707999885082245},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3393000066280365},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.33340001106262207},{"id":"https://openalex.org/C9483764","wikidata":"https://www.wikidata.org/wiki/Q585740","display_name":"Likelihood-ratio test","level":2,"score":0.319599986076355},{"id":"https://openalex.org/C26359558","wikidata":"https://www.wikidata.org/wiki/Q7269462","display_name":"Quasi-maximum likelihood","level":4,"score":0.30640000104904175},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.30239999294281006},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.28360000252723694},{"id":"https://openalex.org/C61420037","wikidata":"https://www.wikidata.org/wiki/Q7316301","display_name":"Restricted maximum likelihood","level":3,"score":0.2818000018596649},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2734000086784363},{"id":"https://openalex.org/C191462741","wikidata":"https://www.wikidata.org/wiki/Q6795902","display_name":"Maximum likelihood sequence estimation","level":3,"score":0.27230000495910645},{"id":"https://openalex.org/C159886148","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov process","level":2,"score":0.27140000462532043},{"id":"https://openalex.org/C196455857","wikidata":"https://www.wikidata.org/wiki/Q5473264","display_name":"Forward algorithm","level":5,"score":0.2630999982357025},{"id":"https://openalex.org/C167928553","wikidata":"https://www.wikidata.org/wiki/Q1376021","display_name":"Estimation theory","level":2,"score":0.26249998807907104},{"id":"https://openalex.org/C54907487","wikidata":"https://www.wikidata.org/wiki/Q7915688","display_name":"Variable-order Markov model","level":4,"score":0.26080000400543213},{"id":"https://openalex.org/C65965080","wikidata":"https://www.wikidata.org/wiki/Q1806885","display_name":"Latent variable model","level":3,"score":0.259799987077713},{"id":"https://openalex.org/C89106044","wikidata":"https://www.wikidata.org/wiki/Q45284","display_name":"Likelihood function","level":3,"score":0.2563999891281128},{"id":"https://openalex.org/C137002209","wikidata":"https://www.wikidata.org/wiki/Q898521","display_name":"Hidden variable theory","level":3,"score":0.2515999972820282}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.csda.2026.108402","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.csda.2026.108402","pdf_url":null,"source":{"id":"https://openalex.org/S132362803","display_name":"Computational Statistics & Data Analysis","issn_l":"0167-9473","issn":["0167-9473","1872-7352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics &amp; Data Analysis","raw_type":"journal-article"},{"id":"pmh:oai:boa.unimib.it:10281/611501","is_oa":true,"landing_page_url":"https://hdl.handle.net/10281/611501","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1016/j.csda.2026.108402","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.csda.2026.108402","pdf_url":null,"source":{"id":"https://openalex.org/S132362803","display_name":"Computational Statistics & Data Analysis","issn_l":"0167-9473","issn":["0167-9473","1872-7352"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics &amp; Data Analysis","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.6478990912437439}],"awards":[{"id":"https://openalex.org/G3389972229","display_name":null,"funder_award_id":"PRIN 2022TZEXKF","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3865340402","display_name":null,"funder_award_id":"CUP J53D23004990006","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6588705221","display_name":null,"funder_award_id":"2022TZEXKF","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null},{"id":"https://openalex.org/F5497039910","display_name":"Ministero dell'Istruzione e del Merito","ror":"https://ror.org/01ehyh486"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1571413698","https://openalex.org/W1950129318","https://openalex.org/W1997330507","https://openalex.org/W2007321142","https://openalex.org/W2020914331","https://openalex.org/W2024637989","https://openalex.org/W2030580999","https://openalex.org/W2032882478","https://openalex.org/W2044394043","https://openalex.org/W2049500688","https://openalex.org/W2049633694","https://openalex.org/W2059279601","https://openalex.org/W2077338494","https://openalex.org/W2090328563","https://openalex.org/W2092566747","https://openalex.org/W2115881827","https://openalex.org/W2129784757","https://openalex.org/W2135046866","https://openalex.org/W2149860264","https://openalex.org/W2154290668","https://openalex.org/W2162845029","https://openalex.org/W2257678991","https://openalex.org/W2408832908","https://openalex.org/W2499351412","https://openalex.org/W2624602871","https://openalex.org/W2747812981","https://openalex.org/W2963018265","https://openalex.org/W3025787433","https://openalex.org/W3165701150","https://openalex.org/W4236076432","https://openalex.org/W4242680994","https://openalex.org/W4281649133","https://openalex.org/W4322761909","https://openalex.org/W4396520949","https://openalex.org/W4412516601"],"related_works":[],"abstract_inverted_index":{"A":[0],"penalized":[1],"maximum":[2],"likelihood":[3,87],"estimation":[4,102,109],"approach":[5,70,90,116],"is":[6,91],"proposed":[7,26,115],"for":[8,71],"discrete-time":[9],"hidden":[10],"Markov":[11],"models":[12],"in":[13,136],"which":[14,50],"the":[15,22,29,57,61,74,80,83,86,114,128,132],"manifest":[16],"distribution":[17],"depends":[18],"on":[19],"covariates":[20],"and":[21,82,104],"lagged":[23],"response.":[24],"The":[25,89],"method":[27],"addresses":[28],"issue":[30],"of":[31,48,56,60,76,79,85,130,134],"latent":[32,62,77],"state":[33],"separation,":[34],"typically":[35],"arising":[36],"with":[37,44,127],"binary":[38],"responses":[39],"or":[40],"categorical":[41],"response":[42],"variables":[43],"a":[45,68,94],"limited":[46],"number":[47,75],"categories,":[49],"leads":[51],"to":[52],"extremely":[53],"large":[54],"estimates":[55],"support":[58],"points":[59],"variable":[63],"distribution.":[64],"We":[65],"also":[66],"propose":[67],"cross-validation":[69],"jointly":[72],"selecting":[73],"states":[78],"model":[81],"strength":[84],"penalization.":[88],"validated":[92],"through":[93],"deep":[95],"simulation":[96],"study":[97],"aimed":[98],"at":[99],"comparing":[100],"parameter":[101],"accuracy":[103],"computational":[105],"efficiency":[106],"across":[107],"different":[108],"procedures.":[110],"Finally,":[111],"we":[112],"illustrate":[113],"by":[117],"analyzing":[118],"longitudinal":[119],"data":[120],"collected":[121],"during":[122],"spinal":[123],"anesthesia,":[124],"including":[125],"covariates,":[126],"aim":[129],"monitoring":[131],"occurrence":[133],"hypotension":[135],"certain":[137],"patients.":[138]},"counts_by_year":[],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2026-05-05T00:00:00"}
