{"id":"https://openalex.org/W3158446859","doi":"https://doi.org/10.1007/s00357-021-09389-2","title":"Matrix Normal Cluster-Weighted Models","display_name":"Matrix Normal Cluster-Weighted Models","publication_year":2021,"publication_date":"2021-06-02","ids":{"openalex":"https://openalex.org/W3158446859","doi":"https://doi.org/10.1007/s00357-021-09389-2","mag":"3158446859"},"language":"en","primary_location":{"id":"doi:10.1007/s00357-021-09389-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00357-021-09389-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00357-021-09389-2.pdf","source":{"id":"https://openalex.org/S73028643","display_name":"Journal of Classification","issn_l":"0176-4268","issn":["0176-4268","1432-1343"],"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":"Journal of Classification","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00357-021-09389-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015878679","display_name":"Salvatore D. Tomarchio","orcid":"https://orcid.org/0000-0003-2690-8546"},"institutions":[{"id":"https://openalex.org/I39063666","display_name":"University of Catania","ror":"https://ror.org/03a64bh57","country_code":"IT","type":"education","lineage":["https://openalex.org/I39063666"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Salvatore D. Tomarchio","raw_affiliation_strings":["Department of Economics and Business, University of Catania, Catania, Italy","(Department of Economics and Business, University of Catania, Catania, Italy)"],"raw_orcid":"https://orcid.org/0000-0003-2690-8546","affiliations":[{"raw_affiliation_string":"Department of Economics and Business, University of Catania, Catania, Italy","institution_ids":["https://openalex.org/I39063666"]},{"raw_affiliation_string":"(Department of Economics and Business, University of Catania, Catania, Italy)","institution_ids":["https://openalex.org/I39063666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5069386158","display_name":"Paul D. McNicholas","orcid":"https://orcid.org/0000-0002-2482-523X"},"institutions":[{"id":"https://openalex.org/I98251732","display_name":"McMaster University","ror":"https://ror.org/02fa3aq29","country_code":"CA","type":"education","lineage":["https://openalex.org/I98251732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Paul D. McNicholas","raw_affiliation_strings":["Department of Mathematics and Statistics, McMaster University, Hamilton, Canada","Department of Mathematics and Statistics , McMaster University , Hamilton, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, McMaster University, Hamilton, Canada","institution_ids":["https://openalex.org/I98251732"]},{"raw_affiliation_string":"Department of Mathematics and Statistics , McMaster University , Hamilton, Canada","institution_ids":["https://openalex.org/I98251732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009939605","display_name":"Antonio Punzo","orcid":"https://orcid.org/0000-0001-7742-1821"},"institutions":[{"id":"https://openalex.org/I39063666","display_name":"University of Catania","ror":"https://ror.org/03a64bh57","country_code":"IT","type":"education","lineage":["https://openalex.org/I39063666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Punzo","raw_affiliation_strings":["Department of Economics and Business, University of Catania, Catania, Italy","(Department of Economics and Business, University of Catania, Catania, Italy)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Economics and Business, University of Catania, Catania, Italy","institution_ids":["https://openalex.org/I39063666"]},{"raw_affiliation_string":"(Department of Economics and Business, University of Catania, Catania, Italy)","institution_ids":["https://openalex.org/I39063666"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015878679"],"corresponding_institution_ids":["https://openalex.org/I39063666"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0533613,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"3","first_page":"556","last_page":"575"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11901","display_name":"Bayesian Methods and Mixture Models","score":0.9998000264167786,"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":0.9998000264167786,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9954000115394592,"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/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9900000095367432,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/covariate","display_name":"Covariate","score":0.8132779598236084},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.5905965566635132},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5830835103988647},{"id":"https://openalex.org/keywords/cluster-analysis","display_name":"Cluster analysis","score":0.572287917137146},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.5371537804603577},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5300975441932678},{"id":"https://openalex.org/keywords/data-set","display_name":"Data set","score":0.4916687607765198},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.4669918119907379},{"id":"https://openalex.org/keywords/grouped-data","display_name":"Grouped data","score":0.4429510831832886},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.42600396275520325},{"id":"https://openalex.org/keywords/conditional-independence","display_name":"Conditional independence","score":0.41222256422042847}],"concepts":[{"id":"https://openalex.org/C119043178","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Covariate","level":2,"score":0.8132779598236084},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.5905965566635132},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5830835103988647},{"id":"https://openalex.org/C73555534","wikidata":"https://www.wikidata.org/wiki/Q622825","display_name":"Cluster analysis","level":2,"score":0.572287917137146},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.5371537804603577},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5300975441932678},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.4916687607765198},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.4669918119907379},{"id":"https://openalex.org/C136336373","wikidata":"https://www.wikidata.org/wiki/Q5611303","display_name":"Grouped data","level":2,"score":0.4429510831832886},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.42600396275520325},{"id":"https://openalex.org/C79772020","wikidata":"https://www.wikidata.org/wiki/Q5159264","display_name":"Conditional independence","level":2,"score":0.41222256422042847}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00357-021-09389-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00357-021-09389-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00357-021-09389-2.pdf","source":{"id":"https://openalex.org/S73028643","display_name":"Journal of Classification","issn_l":"0176-4268","issn":["0176-4268","1432-1343"],"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":"Journal of Classification","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2104.11900","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2104.11900","pdf_url":"https://arxiv.org/pdf/2104.11900","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"mag:3158446859","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2104.11900v1","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:RePEc:spr:jclass:v:38:y:2021:i:3:d:10.1007_s00357-021-09389-2","is_oa":false,"landing_page_url":"http://link.springer.com/10.1007/s00357-021-09389-2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},{"id":"doi:10.48550/arxiv.2104.11900","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2104.11900","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.1007/s00357-021-09389-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00357-021-09389-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00357-021-09389-2.pdf","source":{"id":"https://openalex.org/S73028643","display_name":"Journal of Classification","issn_l":"0176-4268","issn":["0176-4268","1432-1343"],"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":"Journal of Classification","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/8","display_name":"Decent work and economic growth","score":0.6399999856948853}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322690","display_name":"Universit\u00e0 di Catania","ror":"https://ror.org/03a64bh57"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3158446859.pdf","grobid_xml":"https://content.openalex.org/works/W3158446859.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W605692607","https://openalex.org/W749220623","https://openalex.org/W1579271636","https://openalex.org/W1642820549","https://openalex.org/W1774676273","https://openalex.org/W1875932867","https://openalex.org/W1952223965","https://openalex.org/W1967639437","https://openalex.org/W1987837945","https://openalex.org/W2016670387","https://openalex.org/W2023689787","https://openalex.org/W2024476015","https://openalex.org/W2049351438","https://openalex.org/W2049633694","https://openalex.org/W2078537874","https://openalex.org/W2082398846","https://openalex.org/W2086568243","https://openalex.org/W2102723201","https://openalex.org/W2116723563","https://openalex.org/W2135384158","https://openalex.org/W2145007288","https://openalex.org/W2159135906","https://openalex.org/W2162941164","https://openalex.org/W2168175751","https://openalex.org/W2180384296","https://openalex.org/W2345317969","https://openalex.org/W2466214595","https://openalex.org/W2478992108","https://openalex.org/W2488678869","https://openalex.org/W2524681876","https://openalex.org/W2549601578","https://openalex.org/W2582743722","https://openalex.org/W2739929871","https://openalex.org/W2800188602","https://openalex.org/W2809849753","https://openalex.org/W2891760084","https://openalex.org/W2950411888","https://openalex.org/W2961077116","https://openalex.org/W2962730912","https://openalex.org/W2963461702","https://openalex.org/W2963496995","https://openalex.org/W2966562674","https://openalex.org/W2971628054","https://openalex.org/W3044261346","https://openalex.org/W3098381019","https://openalex.org/W3121581836","https://openalex.org/W4235169531"],"related_works":["https://openalex.org/W3171001955","https://openalex.org/W2891760084","https://openalex.org/W2049351438","https://openalex.org/W2742875774","https://openalex.org/W749220623","https://openalex.org/W3138969116","https://openalex.org/W2801210029","https://openalex.org/W2962730912","https://openalex.org/W2770274686","https://openalex.org/W2038842170","https://openalex.org/W3092904269","https://openalex.org/W3022995881","https://openalex.org/W3018199235","https://openalex.org/W3100656227","https://openalex.org/W2968970577","https://openalex.org/W3038373523","https://openalex.org/W2553026194","https://openalex.org/W3125100911","https://openalex.org/W2123046546","https://openalex.org/W3156717680"],"abstract_inverted_index":{"Abstract":[0],"Finite":[1],"mixtures":[2,51],"of":[3,28,37,40,52,88,104,112,142],"regressions":[4,53],"with":[5,17,54],"fixed":[6],"covariates":[7,106,117],"are":[8,90,118,128,152,171],"a":[9,86],"commonly":[10],"used":[11],"model-based":[12],"clustering":[13],"methodology":[14],"to":[15,31,79,120,147],"deal":[16],"regression":[18],"data.":[19,156],"However,":[20],"they":[21],"assume":[22],"assignment":[23],"independence,":[24],"i.e.,":[25],"the":[26,32,38,41,47,67,75,100,105,108,113,116,140,143,149,166],"allocation":[27],"data":[29,84,160],"points":[30,96],"clusters":[33],"is":[34,77],"made":[35],"independently":[36],"distribution":[39,103,111],"covariates.":[42],"To":[43],"take":[44],"into":[45],"account":[46],"latter":[48],"aspect,":[49],"finite":[50],"random":[55],"covariates,":[56],"also":[57],"known":[58],"as":[59],"cluster-weighted":[60],"models":[61],"(CWMs),":[62],"have":[63],"been":[64],"proposed":[65],"in":[66],"univariate":[68],"and":[69,107,139,165],"multivariate":[70],"literature.":[71],"In":[72],"this":[73],"paper,":[74],"CWM":[76],"extended":[78],"matrix":[80,122],"data,":[81],"e.g.,":[82],"those":[83],"where":[85],"set":[87],"variables":[89],"simultaneously":[91],"observed":[92],"at":[93],"different":[94],"time":[95],"or":[97],"locations.":[98],"Specifically,":[99],"cluster-specific":[101,109],"marginal":[102],"conditional":[110],"responses":[114],"given":[115],"assumed":[119],"be":[121],"normal.":[123],"Maximum":[124],"likelihood":[125],"parameter":[126],"estimates":[127],"derived":[129],"using":[130,154],"an":[131],"expectation-conditional":[132],"maximization":[133],"algorithm.":[134],"Parameter":[135],"recovery,":[136],"classification":[137],"assessment,":[138],"capability":[141],"Bayesian":[144],"information":[145],"criterion":[146],"detect":[148],"underlying":[150],"groups":[151],"investigated":[153],"simulated":[155],"Finally,":[157],"two":[158],"real":[159],"applications":[161],"concerning":[162],"educational":[163],"indicators":[164],"Italian":[167],"non-life":[168],"insurance":[169],"market":[170],"presented.":[172]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}