{"id":"https://openalex.org/W7204276192","doi":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","title":"MULTILEVEL ITEM RESPONSE THEORY MODEL USING MML-GHQ METHOD FOR HIERARCHICAL DATA","display_name":"MULTILEVEL ITEM RESPONSE THEORY MODEL USING MML-GHQ METHOD FOR HIERARCHICAL DATA","publication_year":2026,"publication_date":"2026-08-24","ids":{"openalex":"https://openalex.org/W7204276192","doi":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270"},"language":"en","primary_location":{"id":"doi:10.30598/barekengvol20iss4pp3259-3270","doi":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22280/13134","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22280/13134","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068110821","display_name":"Alona Dwinata","orcid":"https://orcid.org/0009-0004-7619-1015","observed_orcids":["https://orcid.org/0009-0004-7619-1015"]},"institutions":[{"id":"https://openalex.org/I21881038","display_name":"IPB University","ror":"https://ror.org/05smgpd89","country_code":"ID","type":"education","lineage":["https://openalex.org/I21881038"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Alona Dwinata","raw_affiliation_strings":["School of Data Science, Mathematics, and Informatics, IPB University, Indonesia"],"raw_orcid":"https://orcid.org/0009-0004-7619-1015","affiliations":[{"raw_affiliation_string":"School of Data Science, Mathematics, and Informatics, IPB University, Indonesia","institution_ids":["https://openalex.org/I21881038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5148229390","display_name":"Anang Kurnia","orcid":"https://orcid.org/0000-0001-9409-2361","observed_orcids":["https://orcid.org/0000-0001-9409-2361"]},"institutions":[{"id":"https://openalex.org/I21881038","display_name":"IPB University","ror":"https://ror.org/05smgpd89","country_code":"ID","type":"education","lineage":["https://openalex.org/I21881038"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Anang Kurnia","raw_affiliation_strings":["School of Data Science, Mathematics, and Informatics, IPB University, Indonesia"],"raw_orcid":"https://orcid.org/0000-0001-9409-2361","affiliations":[{"raw_affiliation_string":"School of Data Science, Mathematics, and Informatics, IPB University, Indonesia","institution_ids":["https://openalex.org/I21881038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5041517012","display_name":"Aji Hamim Wigena","orcid":"https://orcid.org/0009-0008-6723-2347","observed_orcids":["https://orcid.org/0009-0008-6723-2347"]},"institutions":[{"id":"https://openalex.org/I21881038","display_name":"IPB University","ror":"https://ror.org/05smgpd89","country_code":"ID","type":"education","lineage":["https://openalex.org/I21881038"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Aji Hamim Wigena","raw_affiliation_strings":["School of Data Science, Mathematics, and Informatics, IPB University, Indonesia"],"raw_orcid":"https://orcid.org/0009-0008-6723-2347","affiliations":[{"raw_affiliation_string":"School of Data Science, Mathematics, and Informatics, IPB University, Indonesia","institution_ids":["https://openalex.org/I21881038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056440391","display_name":"Muhammad Nur Aidi","orcid":"https://orcid.org/0000-0002-9463-9141","observed_orcids":["https://orcid.org/0000-0002-9463-9141","https://orcid.org/0000-0001-7971-3123"]},"institutions":[{"id":"https://openalex.org/I21881038","display_name":"IPB University","ror":"https://ror.org/05smgpd89","country_code":"ID","type":"education","lineage":["https://openalex.org/I21881038"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Muhammad Nur Aidi","raw_affiliation_strings":["School of Data Science, Mathematics, and Informatics, IPB University, Indonesia"],"raw_orcid":"https://orcid.org/0000-0001-7971-3123","affiliations":[{"raw_affiliation_string":"School of Data Science, Mathematics, and Informatics, IPB University, Indonesia","institution_ids":["https://openalex.org/I21881038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I21881038"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.62944984,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"4","first_page":"3259","last_page":"3270"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10467","display_name":"Psychometric Methodologies and Testing","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10467","display_name":"Psychometric Methodologies and Testing","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.0017999999690800905,"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/T12884","display_name":"Educational Assessment and Pedagogy","score":0.0005000000237487257,"subfield":{"id":"https://openalex.org/subfields/3304","display_name":"Education"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multilevel-item-response-theory","display_name":"multilevel item response theory","score":0.9990000128746033},{"id":"https://openalex.org/keywords/two-parameter-logistic-model","display_name":"two-parameter logistic model","score":0.9610000252723694},{"id":"https://openalex.org/keywords/marginal-maximum-likelihood-estimation","display_name":"marginal maximum likelihood estimation","score":0.8610000014305115},{"id":"https://openalex.org/keywords/gauss-hermite-quadrature","display_name":"Gauss-Hermite quadrature","score":0.9980000257492065},{"id":"https://openalex.org/keywords/hierarchical-data","display_name":"hierarchical data","score":0.796999990940094},{"id":"https://openalex.org/keywords/variance-components","display_name":"variance components","score":0.4410000145435333}],"concepts":[{"id":"https://openalex.org/C19875794","wikidata":"https://www.wikidata.org/wiki/Q1207340","display_name":"Item response theory","level":3,"score":0.7409999966621399},{"id":"https://openalex.org/C53059260","wikidata":"https://www.wikidata.org/wiki/Q374758","display_name":"Multilevel model","level":2,"score":0.6378999948501587},{"id":"https://openalex.org/C2776640315","wikidata":"https://www.wikidata.org/wiki/Q7315941","display_name":"Respondent","level":2,"score":0.6054999828338623},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5248000025749207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4941999912261963},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.43860000371932983},{"id":"https://openalex.org/C144986985","wikidata":"https://www.wikidata.org/wiki/Q871236","display_name":"Hierarchical database model","level":2,"score":0.4374000132083893},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.41110000014305115},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3806999921798706},{"id":"https://openalex.org/C2908647359","wikidata":"https://www.wikidata.org/wiki/Q2625603","display_name":"Population","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.357699990272522},{"id":"https://openalex.org/C151956035","wikidata":"https://www.wikidata.org/wiki/Q1132755","display_name":"Logistic regression","level":2,"score":0.35120001435279846},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3296999931335449},{"id":"https://openalex.org/C16012445","wikidata":"https://www.wikidata.org/wiki/Q1501135","display_name":"Mixed model","level":2,"score":0.3264999985694885},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C20353970","wikidata":"https://www.wikidata.org/wiki/Q1056998","display_name":"Simple random sample","level":3,"score":0.28029999136924744},{"id":"https://openalex.org/C153720581","wikidata":"https://www.wikidata.org/wiki/Q5532490","display_name":"Generalized linear mixed model","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C197656967","wikidata":"https://www.wikidata.org/wiki/Q17058458","display_name":"Marginal model","level":3,"score":0.2689000070095062},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C3018076075","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Variance components","level":2,"score":0.2581000030040741}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.30598/barekengvol20iss4pp3259-3270","doi":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22280/13134","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1e74e099ec0645989fe5ca2234fd0973","doi":null,"is_oa":false,"landing_page_url":"https://doaj.org/article/1e74e099ec0645989fe5ca2234fd0973","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Barekeng, Vol 20, Iss 4 (2026)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.30598/barekengvol20iss4pp3259-3270","doi":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","is_oa":true,"landing_page_url":"https://doi.org/10.30598/barekengvol20iss4pp3259-3270","pdf_url":"https://ojs3.unpatti.ac.id/index.php/barekeng/article/download/22280/13134","source":{"id":"https://openalex.org/S4210230638","display_name":"BAREKENG JURNAL ILMU MATEMATIKA DAN TERAPAN","issn_l":"1978-7227","issn":["1978-7227","2615-3017"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["doaj","jufo-1"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"BAREKENG: Jurnal Ilmu Matematika dan Terapan","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.6164000034332275,"id":"https://metadata.un.org/sdg/4","display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7204276192.pdf","grobid_xml":"https://content.openalex.org/works/W7204276192.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2282772832","https://openalex.org/W7150747493","https://openalex.org/W4399776724","https://openalex.org/W293586629","https://openalex.org/W2031792658","https://openalex.org/W4285493242","https://openalex.org/W3163947212","https://openalex.org/W2090643063","https://openalex.org/W7220205701","https://openalex.org/W2794063191"],"abstract_inverted_index":{"Hierarchical":[0],"item":[1,16,27,43,101,179,258],"response":[2,44,102,259],"data":[3,103,230],"require":[4],"a":[5,39,105,135],"multilevel":[6,42],"approach":[7],"to":[8,25,37,59,82,172],"capture":[9],"the":[10,50,61,71,76,84,162,165,187,220,228,235,240],"diversity":[11],"of":[12,64,75,87,118,137,145,222],"respondent":[13],"abilities":[14,185],"and":[15,23,29,73,94,126,139,152,164,183,198,207,225,249],"characteristics":[17],"by":[18],"separating":[19],"variations":[20],"between":[21],"examinees":[22,110],"schools":[24],"make":[26],"parameter":[28],"ability":[30,85,131,254],"estimates":[31],"more":[32],"precise.":[33],"This":[34,67],"study":[35,68,99],"aims":[36],"develop":[38],"two-parameter":[40],"logistic":[41],"theory":[45],"(MIRT":[46],"2PL)":[47],"model,":[48],"employing":[49],"maximum":[51],"marginal":[52],"likelihood":[53],"method":[54],"with":[55,80,121,234,244],"Gauss-Hermite":[56],"quadrature":[57],"(MML-GHQ)":[58],"estimate":[60],"rank":[62,209],"order":[63],"examinees\u2019":[65,184],"abilities.":[66],"specifically":[69],"investigates":[70],"efficiency":[72],"accuracy":[74],"MIRT":[77,241],"2PL":[78,242],"model":[79,243],"MML-GHQ":[81,204,245],"predict":[83],"rankings":[86,255],"examinees.":[88],"The":[89,97,115,175],"research":[90],"incorporates":[91],"both":[92],"simulated":[93],"empirical":[95,229],"data.":[96,260],"simulation":[98,236],"generated":[100],"under":[104,142,212],"two-level":[106],"hierarchical":[107,257],"structure,":[108],"where":[109],"were":[111,159],"nested":[112],"within":[113],"schools.":[114],"population":[116],"consisted":[117],"50":[119],"schools,":[120,223],"20\u201330":[122],"students":[123],"per":[124],"school":[125,146,214],"five":[127],"items.":[128],"Each":[129],"examinee\u2019s":[130],"was":[132,168,192],"modelled":[133],"as":[134],"combination":[136],"school-level":[138],"individual-level":[140],"effects,":[141],"two":[143],"conditions":[144],"variability:":[147],"high":[148,213],"(\u03c4":[149,154],"=":[150,155],"1.2)":[151],"low":[153],"0.6).":[156],"Random":[157],"samples":[158],"drawn":[160],"from":[161],"population,":[163],"sampling":[166],"process":[167],"repeated":[169],"10":[170],"times":[171],"assess":[173],"consistency.":[174],"analysis":[176],"included":[177],"estimating":[178,253],"parameters,":[180],"variance":[181],"components,":[182],"using":[186,194],"EAP":[188],"approach.":[189],"Model":[190],"performance":[191],"evaluated":[193],"RMSE,":[195],"Spearman":[196],"correlation,":[197],"computation":[199],"time.":[200],"Results":[201],"indicated":[202],"that":[203],"produced":[205],"accurate":[206],"consistent":[208,233],"estimates,":[210],"particularly":[211],"variability.":[215],"Using":[216],"PISA":[217],"data,":[218],"increasing":[219],"number":[221],"students,":[224],"items":[226],"in":[227,256],"yielded":[231],"results":[232],"study.":[237],"In":[238],"conclusion,":[239],"offers":[246],"an":[247],"effective":[248],"efficient":[250],"alternative":[251],"for":[252]},"counts_by_year":[],"updated_date":"2026-10-26T11:51:55.731654","created_date":"2026-08-27T00:00:00"}