{"id":"https://openalex.org/W4407498262","doi":"https://doi.org/10.1007/s11222-025-10579-w","title":"Multilevel latent class models for cross-classified categorical data: model definition and estimation through stochastic EM","display_name":"Multilevel latent class models for cross-classified categorical data: model definition and estimation through stochastic EM","publication_year":2025,"publication_date":"2025-02-13","ids":{"openalex":"https://openalex.org/W4407498262","doi":"https://doi.org/10.1007/s11222-025-10579-w"},"language":"en","primary_location":{"id":"doi:10.1007/s11222-025-10579-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10579-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10579-w.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10579-w.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5031157572","display_name":"Silvia Columbu","orcid":"https://orcid.org/0000-0001-5420-0719"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"S. Columbu","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Cagliari, Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Cagliari, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056596537","display_name":"Nicola Piras","orcid":"https://orcid.org/0000-0002-6338-9354"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"N. Piras","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Cagliari, Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Cagliari, Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032131186","display_name":"Jeroen K. Vermunt","orcid":"https://orcid.org/0000-0001-9053-9330"},"institutions":[{"id":"https://openalex.org/I193700539","display_name":"Tilburg University","ror":"https://ror.org/04b8v1s79","country_code":"NL","type":"education","lineage":["https://openalex.org/I193700539"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"J. K. Vermunt","raw_affiliation_strings":["Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands","institution_ids":["https://openalex.org/I193700539"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5031157572"],"corresponding_institution_ids":["https://openalex.org/I172446870"],"apc_list":{"value":2090,"currency":"EUR","value_usd":2690},"apc_paid":{"value":2090,"currency":"EUR","value_usd":2690},"fwci":2.7411,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.85927315,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"35","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9940000176429749,"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/T10594","display_name":"Genetic and phenotypic traits in livestock","score":0.9818999767303467,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/categorical-variable","display_name":"Categorical variable","score":0.7407635450363159},{"id":"https://openalex.org/keywords/latent-class-model","display_name":"Latent class model","score":0.7151889801025391},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5785714387893677},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5108827948570251},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.5043226480484009},{"id":"https://openalex.org/keywords/estimation","display_name":"Estimation","score":0.492768794298172},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4645777642726898},{"id":"https://openalex.org/keywords/latent-variable","display_name":"Latent variable","score":0.44761568307876587},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4291249215602875},{"id":"https://openalex.org/keywords/mixture-model","display_name":"Mixture model","score":0.41082000732421875},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3895508646965027},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.32662224769592285},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.2834709882736206}],"concepts":[{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.7407635450363159},{"id":"https://openalex.org/C70727504","wikidata":"https://www.wikidata.org/wiki/Q1806878","display_name":"Latent class model","level":2,"score":0.7151889801025391},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5785714387893677},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5108827948570251},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.5043226480484009},{"id":"https://openalex.org/C96250715","wikidata":"https://www.wikidata.org/wiki/Q965330","display_name":"Estimation","level":2,"score":0.492768794298172},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4645777642726898},{"id":"https://openalex.org/C51167844","wikidata":"https://www.wikidata.org/wiki/Q4422623","display_name":"Latent variable","level":2,"score":0.44761568307876587},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4291249215602875},{"id":"https://openalex.org/C61224824","wikidata":"https://www.wikidata.org/wiki/Q2260434","display_name":"Mixture model","level":2,"score":0.41082000732421875},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3895508646965027},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.32662224769592285},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.2834709882736206},{"id":"https://openalex.org/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s11222-025-10579-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10579-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10579-w.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},{"id":"pmh:oai:tilburguniversity.edu:openaire_cris_publications/b2eb18be-ea63-4263-9b85-11543b443731","is_oa":true,"landing_page_url":"https://research.tilburguniversity.edu/en/publications/b2eb18be-ea63-4263-9b85-11543b443731","pdf_url":null,"source":{"id":"https://openalex.org/S4406923027","display_name":"Tilburg University Research Portal","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Columbu, S, Piras, N & Vermunt, J K 2025, 'Multilevel latent class models for cross-classified categorical data : model definition and estimation through stochastic EM', Statistics and Computing, vol. 35, no. 2, 50. https://doi.org/10.1007/s11222-025-10579-w","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:iris.unica.it:11584/445528","is_oa":true,"landing_page_url":"https://link.springer.com/article/10.1007/s11222-025-10579-w","pdf_url":null,"source":{"id":"https://openalex.org/S4377196293","display_name":"UNICA IRIS Institutional Research Information System (University of Cagliari)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172446870","host_organization_name":"University of Cagliari","host_organization_lineage":["https://openalex.org/I172446870"],"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:10.1007/s11222-025-10579-w","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11222-025-10579-w","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11222-025-10579-w.pdf","source":{"id":"https://openalex.org/S5437875","display_name":"Statistics and Computing","issn_l":"0960-3174","issn":["0960-3174","1573-1375"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Statistics and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320313987","display_name":"Universit\u00e0 degli Studi di Cagliari","ror":"https://ror.org/003109y17"},{"id":"https://openalex.org/F4320315324","display_name":"Fondazione di Sardegna","ror":"https://ror.org/02sryfh37"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407498262.pdf","grobid_xml":"https://content.openalex.org/works/W4407498262.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1528177290","https://openalex.org/W1604544535","https://openalex.org/W1966129222","https://openalex.org/W1982509351","https://openalex.org/W1982882480","https://openalex.org/W2007761454","https://openalex.org/W2015307819","https://openalex.org/W2018516812","https://openalex.org/W2049633694","https://openalex.org/W2050341350","https://openalex.org/W2053742104","https://openalex.org/W2087232522","https://openalex.org/W2093895222","https://openalex.org/W2102907934","https://openalex.org/W2118360516","https://openalex.org/W2155377619","https://openalex.org/W2287982579","https://openalex.org/W2498094064","https://openalex.org/W2500845915","https://openalex.org/W2794266768","https://openalex.org/W2896706527","https://openalex.org/W3124427131","https://openalex.org/W3214570248","https://openalex.org/W4241635929","https://openalex.org/W4295365628","https://openalex.org/W4385612139","https://openalex.org/W4399783659"],"related_works":["https://openalex.org/W2944501335","https://openalex.org/W2130110160","https://openalex.org/W1603253275","https://openalex.org/W1501016332","https://openalex.org/W155768060","https://openalex.org/W1604273845","https://openalex.org/W4230230730","https://openalex.org/W1535265092","https://openalex.org/W1522817657","https://openalex.org/W2165807738"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"present":[2],"an":[3,127,166],"extension":[4],"of":[5,69,74,85,95,108,135,141,153,159,172,188],"the":[6,46,75,86,92,96,109,115,122,136,157,160,170],"multilevel":[7,14],"latent":[8,49],"class":[9,50],"model":[10,110,162],"for":[11,32,60,72,80,112],"dealing":[12],"with":[13,179],"cross-classified":[15,93],"categorical":[16],"data.":[17],"Cross-classified":[18],"data":[19],"structures":[20],"arise":[21],"when":[22],"observations":[23],"are":[24],"simultaneously":[25],"nested":[26,35,182],"within":[27,36],"two":[28,57],"or":[29],"more":[30],"groups,":[31],"example,":[33,113],"children":[34,61],"both":[37,184],"schools":[38,81],"and":[39,62,82,186],"neighborhoods.":[40,83],"More":[41],"specifically,":[42],"we":[43,125],"propose":[44,126],"extending":[45],"standard":[47],"hierarchical":[48],"model,":[51],"which":[52,144],"contains":[53],"mixture":[54,70],"components":[55,71],"at":[56,175],"levels,":[58],"say":[59,79],"schools,":[63],"by":[64],"including":[65],"a":[66,119,132,151],"separate":[67],"set":[68,152],"each":[73],"higher-level":[76],"crossed":[77],"classifications,":[78],"Because":[84],"complex":[87],"dependency":[88],"structure":[89],"arising":[90],"from":[91],"nature":[94],"data,":[97],"it":[98],"is":[99,163],"no":[100],"longer":[101],"possible":[102],"to":[103,121],"obtain":[104],"maximum":[105],"likelihood":[106],"estimates":[107],"parameters,":[111],"using":[114,131,165],"EM":[116,137],"algorithm.":[117,138],"As":[118],"solution":[120],"estimation":[123,129],"problem,":[124],"approximate":[128],"approach":[130],"stochastic":[133],"version":[134],"The":[139],"performance":[140],"this":[142],"approach,":[143],"resembles":[145],"Gibbs":[146],"sampling,":[147],"was":[148],"investigated":[149],"through":[150],"simulation":[154],"studies.":[155],"Moreover,":[156],"application":[158],"new":[161],"illustrated":[164],"Italian":[167],"dataset":[168],"on":[169],"quality":[171],"university":[173],"experience":[174],"degree":[176,180],"programme":[177],"level,":[178],"programmes":[181],"in":[183],"universities":[185],"fields":[187],"study.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}