{"id":"https://openalex.org/W1600728323","doi":"https://doi.org/10.1007/s00180-009-0164-x","title":"On the convergence of the partial least squares path modeling algorithm","display_name":"On the convergence of the partial least squares path modeling algorithm","publication_year":2009,"publication_date":"2009-07-31","ids":{"openalex":"https://openalex.org/W1600728323","doi":"https://doi.org/10.1007/s00180-009-0164-x","mag":"1600728323"},"language":"en","primary_location":{"id":"doi:10.1007/s00180-009-0164-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-009-0164-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-009-0164-x.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","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/s00180-009-0164-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008753312","display_name":"J\u00f6rg Henseler","orcid":"https://orcid.org/0000-0002-9736-3048"},"institutions":[{"id":"https://openalex.org/I145872427","display_name":"Radboud University Nijmegen","ror":"https://ror.org/016xsfp80","country_code":"NL","type":"education","lineage":["https://openalex.org/I145872427"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"J\u00f6rg Henseler","raw_affiliation_strings":["Institute for Management Research, Radboud University Nijmegen, PO Box 9108, 6500 HK, Nijmegen, The Netherlands","Radboud University Nijmegen, Institute for Management Research, PO Box 9108, 6500 HK Nijmegen, The Netherlands"],"affiliations":[{"raw_affiliation_string":"Institute for Management Research, Radboud University Nijmegen, PO Box 9108, 6500 HK, Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]},{"raw_affiliation_string":"Radboud University Nijmegen, Institute for Management Research, PO Box 9108, 6500 HK Nijmegen, The Netherlands","institution_ids":["https://openalex.org/I145872427"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008753312"],"corresponding_institution_ids":["https://openalex.org/I145872427"],"apc_list":{"value":2490,"currency":"EUR","value_usd":3090},"apc_paid":{"value":2490,"currency":"EUR","value_usd":3090},"fwci":0.7654,"has_fulltext":true,"cited_by_count":25,"citation_normalized_percentile":{"value":0.75042113,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"25","issue":"1","first_page":"107","last_page":"120"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14474","display_name":"Industrial Technology and Control Systems","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T14474","display_name":"Industrial Technology and Control Systems","score":0.9817000031471252,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14249","display_name":"Water Quality Monitoring and Analysis","score":0.9467999935150146,"subfield":{"id":"https://openalex.org/subfields/2311","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T14446","display_name":"Civil and Geotechnical Engineering Research","score":0.9192000031471252,"subfield":{"id":"https://openalex.org/subfields/2200","display_name":"General Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/path","display_name":"Path (computing)","score":0.7638763189315796},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7319228649139404},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6843400597572327},{"id":"https://openalex.org/keywords/partial-least-squares-regression","display_name":"Partial least squares regression","score":0.6634455919265747},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5602014064788818},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5060788989067078},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44122880697250366},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4244231879711151},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.4118528962135315},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3629733920097351},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.15145784616470337}],"concepts":[{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.7638763189315796},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7319228649139404},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6843400597572327},{"id":"https://openalex.org/C22354355","wikidata":"https://www.wikidata.org/wiki/Q422009","display_name":"Partial least squares regression","level":2,"score":0.6634455919265747},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5602014064788818},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5060788989067078},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44122880697250366},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4244231879711151},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.4118528962135315},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3629733920097351},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.15145784616470337},{"id":"https://openalex.org/C126838900","wikidata":"https://www.wikidata.org/wiki/Q77604","display_name":"Radiology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":5,"locations":[{"id":"doi:10.1007/s00180-009-0164-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-009-0164-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-009-0164-x.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:spr:compst:v:25:y:2010:i:1:p:107-120","is_oa":false,"landing_page_url":"http://hdl.handle.net/10.1007/s00180-009-0164-x","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":"pmh:oai:repository.ubn.ru.nl:2066/87013","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/87013","pdf_url":null,"source":{"id":"https://openalex.org/S4306401067","display_name":"Radboud Repository (Radboud University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145872427","host_organization_name":"Radboud University Nijmegen","host_organization_lineage":["https://openalex.org/I145872427"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:ru:oai:repository.ubn.ru.nl:2066/160878","is_oa":false,"landing_page_url":"http://hdl.handle.net/2066/160878","pdf_url":null,"source":{"id":"https://openalex.org/S4306401843","display_name":"Data Archiving and Networked Services (DANS)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1322597698","host_organization_name":"Royal Netherlands Academy of Arts and Sciences","host_organization_lineage":["https://openalex.org/I1322597698"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Martens, H.; Naes, T. (ed.), Proceedings of PLS\u201907 \u2013 The 5th International Symposium on PLS and Related Methods, 57 - 61. As, Norwegen : [S.n.]","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:1600728323","is_oa":false,"landing_page_url":"https://www.narcis.nl/publication/RecordID/oai%3Arepository.ubn.ru.nl%3A2066%2F160878","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s00180-009-0164-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00180-009-0164-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00180-009-0164-x.pdf","source":{"id":"https://openalex.org/S8500805","display_name":"Computational Statistics","issn_l":"0943-4062","issn":["0943-4062","1613-9658"],"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-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Statistics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1600728323.pdf","grobid_xml":"https://content.openalex.org/works/W1600728323.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W169042837","https://openalex.org/W1550181012","https://openalex.org/W1584405424","https://openalex.org/W1963991144","https://openalex.org/W1970105865","https://openalex.org/W1970794614","https://openalex.org/W1984947418","https://openalex.org/W1986092722","https://openalex.org/W2014134373","https://openalex.org/W2024968021","https://openalex.org/W2030431067","https://openalex.org/W2049159124","https://openalex.org/W2056877034","https://openalex.org/W2063159792","https://openalex.org/W2071761220","https://openalex.org/W2090552208","https://openalex.org/W2093109772","https://openalex.org/W2098685541","https://openalex.org/W2134816404","https://openalex.org/W2796176660","https://openalex.org/W3023964749","https://openalex.org/W4251225833","https://openalex.org/W4251955157"],"related_works":["https://openalex.org/W2001768043","https://openalex.org/W1599263795","https://openalex.org/W2377803320","https://openalex.org/W2034779475","https://openalex.org/W2971816392","https://openalex.org/W2044504412","https://openalex.org/W2904519850","https://openalex.org/W2352346100","https://openalex.org/W2361689554","https://openalex.org/W2187792181","https://openalex.org/W3117342589","https://openalex.org/W2776668752","https://openalex.org/W2410040779","https://openalex.org/W2396828366","https://openalex.org/W2506049532","https://openalex.org/W2117376768","https://openalex.org/W2206383733","https://openalex.org/W2010524355","https://openalex.org/W2117340015","https://openalex.org/W216230010"],"abstract_inverted_index":{"This":[0,50],"paper":[1,51],"adds":[2],"to":[3,92,94],"an":[4],"important":[5],"aspect":[6],"of":[7,17,47,55,57,85,97,107],"Partial":[8],"Least":[9],"Squares":[10],"(PLS)":[11],"path":[12,21,40,60,77],"modeling,":[13],"namely":[14],"the":[15,18,58,72,76,86],"convergence":[16,98],"iterative":[19],"PLS":[20,29,59,108],"modeling":[22,61],"algorithm.":[23,62,87],"Whilst":[24],"conventional":[25],"wisdom":[26],"says":[27],"that":[28],"always":[30],"converges":[31],"in":[32],"practice,":[33],"there":[34],"is":[35],"no":[36],"formal":[37],"proof":[38,96],"for":[39],"models":[41],"with":[42,71],"more":[43],"than":[44],"two":[45,82],"blocks":[46],"manifest":[48],"variables.":[49],"presents":[52],"six":[53],"cases":[54,64],"non-convergence":[56],"These":[63],"were":[65],"estimated":[66],"using":[67],"Mode":[68],"A":[69],"combined":[70],"factorial":[73],"scheme":[74],"or":[75],"weighting":[78],"scheme,":[79],"which":[80],"are":[81],"popular":[83],"options":[84],"As":[88],"a":[89,95],"conclusion,":[90],"efforts":[91],"come":[93],"under":[99],"these":[100],"schemes":[101],"can":[102],"be":[103],"abandoned,":[104],"and":[105],"users":[106],"should":[109],"triangulate":[110],"their":[111],"estimation":[112],"results.":[113]},"counts_by_year":[{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}