{"id":"https://openalex.org/W4313407436","doi":"https://doi.org/10.3390/sym14122687","title":"A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application","display_name":"A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application","publication_year":2022,"publication_date":"2022-12-19","ids":{"openalex":"https://openalex.org/W4313407436","doi":"https://doi.org/10.3390/sym14122687"},"language":"en","primary_location":{"id":"doi:10.3390/sym14122687","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122687","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2687/pdf?version=1671584454","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/12/2687/pdf?version=1671584454","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028719974","display_name":"Idhia Sriliana","orcid":"https://orcid.org/0000-0003-3926-4129"},"institutions":[{"id":"https://openalex.org/I166843116","display_name":"Sepuluh Nopember Institute of Technology","ror":"https://ror.org/05kbmmt89","country_code":"ID","type":"education","lineage":["https://openalex.org/I166843116"]},{"id":"https://openalex.org/I47755478","display_name":"University of Bengkulu","ror":"https://ror.org/04w077t62","country_code":"ID","type":"education","lineage":["https://openalex.org/I47755478"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Idhia Sriliana","raw_affiliation_strings":["Department of Statistics, Faculty of Mathematics and Natural Sciences, University of Bengkulu, Bengkulu 38371, Indonesia","Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"],"raw_orcid":"https://orcid.org/0000-0003-3926-4129","affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Mathematics and Natural Sciences, University of Bengkulu, Bengkulu 38371, Indonesia","institution_ids":["https://openalex.org/I47755478"]},{"raw_affiliation_string":"Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia","institution_ids":["https://openalex.org/I166843116"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5012999018","display_name":"I Nyoman Budiantara","orcid":"https://orcid.org/0000-0001-6572-4083"},"institutions":[{"id":"https://openalex.org/I166843116","display_name":"Sepuluh Nopember Institute of Technology","ror":"https://ror.org/05kbmmt89","country_code":"ID","type":"education","lineage":["https://openalex.org/I166843116"]}],"countries":["ID"],"is_corresponding":true,"raw_author_name":"I Nyoman Budiantara","raw_affiliation_strings":["Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"],"raw_orcid":"https://orcid.org/0000-0001-6572-4083","affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia","institution_ids":["https://openalex.org/I166843116"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024483933","display_name":"Vita Ratnasari","orcid":"https://orcid.org/0000-0002-7579-4752"},"institutions":[{"id":"https://openalex.org/I166843116","display_name":"Sepuluh Nopember Institute of Technology","ror":"https://ror.org/05kbmmt89","country_code":"ID","type":"education","lineage":["https://openalex.org/I166843116"]}],"countries":["ID"],"is_corresponding":false,"raw_author_name":"Vita Ratnasari","raw_affiliation_strings":["Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Surabaya 60111, Indonesia","institution_ids":["https://openalex.org/I166843116"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5012999018"],"corresponding_institution_ids":["https://openalex.org/I166843116"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":1.4954,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.87625361,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":98},"biblio":{"volume":"14","issue":"12","first_page":"2687","last_page":"2687"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9639999866485596,"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"}},"topics":[{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9639999866485596,"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"}},{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.9523000121116638,"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":0.9365000128746033,"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/estimator","display_name":"Estimator","score":0.7381016612052917},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6375417709350586},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5717103481292725},{"id":"https://openalex.org/keywords/nonparametric-regression","display_name":"Nonparametric regression","score":0.552489697933197},{"id":"https://openalex.org/keywords/nonparametric-statistics","display_name":"Nonparametric statistics","score":0.5319523811340332},{"id":"https://openalex.org/keywords/spline","display_name":"Spline (mechanical)","score":0.47482332587242126},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.3440595865249634}],"concepts":[{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.7381016612052917},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6375417709350586},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5717103481292725},{"id":"https://openalex.org/C74127309","wikidata":"https://www.wikidata.org/wiki/Q3455886","display_name":"Nonparametric regression","level":3,"score":0.552489697933197},{"id":"https://openalex.org/C102366305","wikidata":"https://www.wikidata.org/wiki/Q1097688","display_name":"Nonparametric statistics","level":2,"score":0.5319523811340332},{"id":"https://openalex.org/C10390562","wikidata":"https://www.wikidata.org/wiki/Q581809","display_name":"Spline (mechanical)","level":2,"score":0.47482332587242126},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3440595865249634},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14122687","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122687","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2687/pdf?version=1671584454","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:93e8e8b445ae44acb125ded2991900a4","is_oa":true,"landing_page_url":"https://doaj.org/article/93e8e8b445ae44acb125ded2991900a4","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,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 12, p 2687 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/12/2687/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14122687","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"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":"Symmetry; Volume 14; Issue 12; Pages: 2687","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14122687","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14122687","pdf_url":"https://www.mdpi.com/2073-8994/14/12/2687/pdf?version=1671584454","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"No poverty","score":0.800000011920929,"id":"https://metadata.un.org/sdg/1"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4313407436.pdf"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1423766661","https://openalex.org/W1582606351","https://openalex.org/W1990866660","https://openalex.org/W1992272072","https://openalex.org/W2024658605","https://openalex.org/W2047463875","https://openalex.org/W2068974129","https://openalex.org/W2128552636","https://openalex.org/W2141276436","https://openalex.org/W2168350083","https://openalex.org/W2288868464","https://openalex.org/W2343177916","https://openalex.org/W2395212820","https://openalex.org/W2510088525","https://openalex.org/W2518687982","https://openalex.org/W2520309442","https://openalex.org/W2557575723","https://openalex.org/W2560157848","https://openalex.org/W2898762627","https://openalex.org/W2962937842","https://openalex.org/W2973202046","https://openalex.org/W3006505822","https://openalex.org/W3093358629","https://openalex.org/W3094322889","https://openalex.org/W3159179914","https://openalex.org/W3160210471","https://openalex.org/W3177175209","https://openalex.org/W3186764078","https://openalex.org/W3209957588","https://openalex.org/W4282549078","https://openalex.org/W4289177604","https://openalex.org/W4298876635","https://openalex.org/W4302599714","https://openalex.org/W4386877197","https://openalex.org/W4388319941","https://openalex.org/W6684808322","https://openalex.org/W6712075449","https://openalex.org/W6725447246","https://openalex.org/W6726503845","https://openalex.org/W6726768600","https://openalex.org/W6756165532","https://openalex.org/W6856207162"],"related_works":["https://openalex.org/W2111545434","https://openalex.org/W4381052368","https://openalex.org/W1541412963","https://openalex.org/W1843324721","https://openalex.org/W3141138882","https://openalex.org/W2184572292","https://openalex.org/W1509119367","https://openalex.org/W2170349014","https://openalex.org/W4321367829","https://openalex.org/W2041704562"],"abstract_inverted_index":{"Longitudinal":[0],"data":[1,40,63,171,194],"modeling":[2,41,172],"is":[3,15],"widely":[4],"carried":[5],"out":[6],"using":[7,42,64],"parametric":[8,13],"methods.":[9],"However,":[10],"when":[11],"the":[12,17,57,87,92,101,111,122,134,146,149,155,158,175,179,183,188,193],"model":[14,117,185,190],"misspecified,":[16],"obtained":[18],"estimator":[19,45,165],"might":[20],"be":[21],"severely":[22],"biased":[23],"and":[24,70,161],"lead":[25],"to":[26,55,85,129,144,154],"erroneous":[27],"conclusions.":[28],"In":[29],"this":[30,52],"study,":[31],"we":[32],"propose":[33],"a":[34,43,79,104,130],"new":[35],"estimation":[36,81,90],"method":[37,77],"for":[38,61,97],"longitudinal":[39,62,102,131,170],"mixed":[44,151,164],"in":[46,100,110,138,169],"nonparametric":[47,58],"regression.":[48],"The":[49,73,115],"objective":[50],"of":[51,91,133,148,182],"study":[53],"was":[54,83,108,118,142],"estimate":[56],"regression":[59,88,112],"curve":[60,89,113],"two":[65],"combined":[66],"estimators:":[67],"truncated":[68,159],"spline":[69,160],"local":[71,162],"linear.":[72],"weighted":[74],"least":[75],"square":[76],"with":[78],"two-stage":[80],"procedure":[82],"used":[84],"obtain":[86],"proposed":[93,150,189],"model.":[94],"To":[95],"account":[96],"within-subject":[98],"correlations":[99],"data,":[103],"symmetric":[105],"weight":[106],"matrix":[107],"given":[109],"estimation.":[114],"best":[116,184],"determined":[119],"by":[120],"minimizing":[121],"generalized":[123],"cross-validation":[124],"value.":[125,177],"Furthermore,":[126],"an":[127],"application":[128],"dataset":[132],"poverty":[135],"gap":[136],"index":[137],"Bengkulu":[139],"Province,":[140],"Indonesia,":[141],"conducted":[143],"illustrate":[145],"performance":[147,168],"estimator.":[152],"Compared":[153],"single":[156],"estimator,":[157],"linear":[163],"had":[166],"better":[167],"based":[173],"on":[174],"GCV":[176],"Additionally,":[178],"empirical":[180],"results":[181],"indicated":[186],"that":[187],"could":[191],"explain":[192],"variation":[195],"exceptionally":[196],"well.":[197]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2023-01-06T00:00:00"}
