{"id":"https://openalex.org/W4407082215","doi":"https://doi.org/10.3390/e27020161","title":"Fiducial Inference in Linear Mixed-Effects Models","display_name":"Fiducial Inference in Linear Mixed-Effects Models","publication_year":2025,"publication_date":"2025-02-03","ids":{"openalex":"https://openalex.org/W4407082215","doi":"https://doi.org/10.3390/e27020161","pmid":"https://pubmed.ncbi.nlm.nih.gov/40003158"},"language":"en","primary_location":{"id":"doi:10.3390/e27020161","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020161","pdf_url":"https://www.mdpi.com/1099-4300/27/2/161/pdf?version=1738573694","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/27/2/161/pdf?version=1738573694","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100404947","display_name":"Jie Yang","orcid":"https://orcid.org/0000-0003-4801-7162"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jie Yang","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100678724","display_name":"Xinmin Li","orcid":"https://orcid.org/0000-0002-2573-5236"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xinmin Li","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101683410","display_name":"Hongwei Gao","orcid":"https://orcid.org/0000-0001-7691-2071"},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongwei Gao","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090038262","display_name":"Chenchen Zou","orcid":null},"institutions":[{"id":"https://openalex.org/I108688024","display_name":"Qingdao University","ror":"https://ror.org/021cj6z65","country_code":"CN","type":"education","lineage":["https://openalex.org/I108688024"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chenchen Zou","raw_affiliation_strings":["School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China","institution_ids":["https://openalex.org/I108688024"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5090038262"],"corresponding_institution_ids":["https://openalex.org/I108688024"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":2.8314,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.859343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"161","last_page":"161"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9993000030517578,"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":0.9993000030517578,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9968000054359436,"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/T10841","display_name":"Economic and Environmental Valuation","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/fiducial-marker","display_name":"Fiducial marker","score":0.792689859867096},{"id":"https://openalex.org/keywords/fiducial-inference","display_name":"Fiducial inference","score":0.7259987592697144},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.6385385990142822},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5342691540718079},{"id":"https://openalex.org/keywords/bayesian-probability","display_name":"Bayesian probability","score":0.5225455164909363},{"id":"https://openalex.org/keywords/bayesian-inference","display_name":"Bayesian inference","score":0.5129756331443787},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.49088793992996216},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.48944154381752014},{"id":"https://openalex.org/keywords/frequentist-inference","display_name":"Frequentist inference","score":0.4560433030128479},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.4523714780807495},{"id":"https://openalex.org/keywords/random-effects-model","display_name":"Random effects model","score":0.44398626685142517},{"id":"https://openalex.org/keywords/confidence-interval","display_name":"Confidence interval","score":0.42435723543167114},{"id":"https://openalex.org/keywords/generalized-linear-mixed-model","display_name":"Generalized linear mixed model","score":0.42311906814575195},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4120601415634155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32423752546310425},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.1970067322254181}],"concepts":[{"id":"https://openalex.org/C173974348","wikidata":"https://www.wikidata.org/wiki/Q1469893","display_name":"Fiducial marker","level":2,"score":0.792689859867096},{"id":"https://openalex.org/C95167961","wikidata":"https://www.wikidata.org/wiki/Q4483495","display_name":"Fiducial inference","level":5,"score":0.7259987592697144},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.6385385990142822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5342691540718079},{"id":"https://openalex.org/C107673813","wikidata":"https://www.wikidata.org/wiki/Q812534","display_name":"Bayesian probability","level":2,"score":0.5225455164909363},{"id":"https://openalex.org/C160234255","wikidata":"https://www.wikidata.org/wiki/Q812535","display_name":"Bayesian inference","level":3,"score":0.5129756331443787},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.49088793992996216},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.48944154381752014},{"id":"https://openalex.org/C162376815","wikidata":"https://www.wikidata.org/wiki/Q2158281","display_name":"Frequentist inference","level":4,"score":0.4560433030128479},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.4523714780807495},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.44398626685142517},{"id":"https://openalex.org/C44249647","wikidata":"https://www.wikidata.org/wiki/Q208498","display_name":"Confidence interval","level":2,"score":0.42435723543167114},{"id":"https://openalex.org/C153720581","wikidata":"https://www.wikidata.org/wiki/Q5532490","display_name":"Generalized linear mixed model","level":2,"score":0.42311906814575195},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4120601415634155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32423752546310425},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.1970067322254181},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C95190672","wikidata":"https://www.wikidata.org/wiki/Q815382","display_name":"Meta-analysis","level":2,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/e27020161","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020161","pdf_url":"https://www.mdpi.com/1099-4300/27/2/161/pdf?version=1738573694","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmid:40003158","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/40003158","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy (Basel, Switzerland)","raw_type":null},{"id":"pmh:oai:pubmedcentral.nih.gov:11854194","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11854194","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11854194/pdf/entropy-27-00161.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"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":"Entropy (Basel)","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:db273ee1d970436789dcbc041f391adf","is_oa":true,"landing_page_url":"https://doaj.org/article/db273ee1d970436789dcbc041f391adf","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 27, Iss 2, p 161 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/e27020161","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e27020161","pdf_url":"https://www.mdpi.com/1099-4300/27/2/161/pdf?version=1738573694","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5335186619","display_name":null,"funder_award_id":"11871294","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5917278180","display_name":null,"funder_award_id":"72171126","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6099205513","display_name":null,"funder_award_id":"11901328","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407082215.pdf","grobid_xml":"https://content.openalex.org/works/W4407082215.grobid-xml"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1951724000","https://openalex.org/W1990646909","https://openalex.org/W2005588530","https://openalex.org/W2014581807","https://openalex.org/W2047415626","https://openalex.org/W2059251872","https://openalex.org/W2076881231","https://openalex.org/W2088724118","https://openalex.org/W2094761105","https://openalex.org/W2140773653","https://openalex.org/W2141895117","https://openalex.org/W2149719430","https://openalex.org/W2314561345","https://openalex.org/W2326809886","https://openalex.org/W2749069611","https://openalex.org/W2774486220","https://openalex.org/W2787428250","https://openalex.org/W2795510560","https://openalex.org/W2962703949","https://openalex.org/W2982375972","https://openalex.org/W3100080797","https://openalex.org/W3131434759","https://openalex.org/W4248747394","https://openalex.org/W4388297583","https://openalex.org/W6651974960","https://openalex.org/W6749982788","https://openalex.org/W6769259465"],"related_works":["https://openalex.org/W3102972421","https://openalex.org/W4322760254","https://openalex.org/W2478683457","https://openalex.org/W4235385816","https://openalex.org/W3111430230","https://openalex.org/W4251525937","https://openalex.org/W2884750441","https://openalex.org/W2039912667","https://openalex.org/W4239322872","https://openalex.org/W4309301408"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,34,49,75],"novel":[3],"framework":[4],"for":[5,89,96,123],"fiducial":[6,25,58,81],"inference":[7,66,122],"in":[8,46,74],"linear":[9],"mixed-effects":[10],"(LME)":[11],"models,":[12],"with":[13,52,132],"the":[14,30,39,56,65,124,133],"standard":[15],"deviation":[16],"of":[17,33,67,126],"random":[18,68,127],"effects":[19,69,128],"reformulated":[20],"as":[21,29],"coefficients.":[22],"The":[23,42],"exact":[24],"density":[26,43],"is":[27,44,93],"derived":[28],"equilibrium":[31],"measure":[32],"reversible":[35],"Markov":[36],"chain":[37],"over":[38],"parameter":[40],"space.":[41],"equivalent":[45],"form":[47],"to":[48,63,111],"Bayesian":[50,115],"LME":[51,82],"noninformative":[53],"prior,":[54],"while":[55],"underlying":[57],"structure":[59],"adds":[60],"new":[61],"benefits":[62],"unify":[64],"and":[70,77,92,102,116],"all":[71],"other":[72],"parameters":[73],"neat":[76],"simultaneous":[78],"way.":[79],"Our":[80],"needs":[83],"no":[84],"additional":[85],"tests":[86],"or":[87],"statistics":[88],"zero":[90],"variance":[91,125],"more":[94],"suitable":[95],"small":[97],"sample":[98],"sizes.":[99],"In":[100],"simulation":[101],"empirical":[103],"analysis,":[104],"our":[105,121],"confidence":[106],"intervals":[107],"(CIs)":[108],"are":[109],"comparable":[110],"those":[112],"based":[113],"on":[114],"likelihood":[117,134],"profiling":[118],"methods.":[119],"And":[120],"has":[129],"competitive":[130],"power":[131],"ratio":[135],"test.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-03-13T14:20:09.374765","created_date":"2025-10-10T00:00:00"}