{"id":"https://openalex.org/W2885565440","doi":"https://doi.org/10.1177/0081175018789441","title":"Nonlinear Autoregressive Latent Trajectory Models","display_name":"Nonlinear Autoregressive Latent Trajectory Models","publication_year":2018,"publication_date":"2018-08-01","ids":{"openalex":"https://openalex.org/W2885565440","doi":"https://doi.org/10.1177/0081175018789441","mag":"2885565440","pmid":"https://pubmed.ncbi.nlm.nih.gov/31427831","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/6699169"},"language":"en","primary_location":{"id":"doi:10.1177/0081175018789441","doi":"https://doi.org/10.1177/0081175018789441","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0081175018789441","pdf_url":null,"source":{"id":"https://openalex.org/S181883320","display_name":"Sociological Methodology","issn_l":"0081-1750","issn":["0081-1750","1467-9531"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","jufo-2","ki-jl-2","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sociological Methodology","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6699169","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002233206","display_name":"Shawn Bauldry","orcid":"https://orcid.org/0000-0002-6679-3125","observed_orcids":["https://orcid.org/0000-0002-6679-3125"]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Shawn Bauldry","raw_affiliation_strings":["Purdue University, West Lafayette, IN, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University, West Lafayette, IN, USA","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047232270","display_name":"Kenneth A. Bollen","orcid":"https://orcid.org/0000-0002-6710-3800","observed_orcids":["https://orcid.org/0000-0002-6710-3800"]},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kenneth A. Bollen","raw_affiliation_strings":["University of North Carolina at Chapel Hill, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of North Carolina at Chapel Hill, USA","institution_ids":["https://openalex.org/I114027177"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5002233206"],"corresponding_institution_ids":["https://openalex.org/I219193219"],"apc_list":{"value":3650,"currency":"USD","value_usd":3650},"apc_paid":null,"fwci":1.2352,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.82225272,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"48","issue":"1","first_page":"269","last_page":"302"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.6460000276565552,"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":0.6460000276565552,"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/T10467","display_name":"Psychometric Methodologies and Testing","score":0.295199990272522,"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/T13141","display_name":"Statistical Methods and Applications","score":0.009600000455975533,"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/quadratic-growth","display_name":"quadratic growth","score":0.7820000052452087},{"id":"https://openalex.org/keywords/system-identification","display_name":"system identification","score":0.9480000138282776},{"id":"https://openalex.org/keywords/parameter-interpretation","display_name":"parameter interpretation","score":0.6669999957084656},{"id":"https://openalex.org/keywords/model-comparison","display_name":"model comparison","score":0.5730000138282776},{"id":"https://openalex.org/keywords/estimation-bias","display_name":"estimation bias","score":0.515999972820282},{"id":"https://openalex.org/keywords/longitudinal-data","display_name":"longitudinal data","score":0.39100000262260437}],"concepts":[{"id":"https://openalex.org/C159877910","wikidata":"https://www.wikidata.org/wiki/Q2202883","display_name":"Autoregressive model","level":2,"score":0.8098130822181702},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5936651825904846},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5883510708808899},{"id":"https://openalex.org/C42536954","wikidata":"https://www.wikidata.org/wiki/Q7049462","display_name":"Nonlinear autoregressive exogenous model","level":3,"score":0.5729897022247314},{"id":"https://openalex.org/C194657046","wikidata":"https://www.wikidata.org/wiki/Q7394685","display_name":"STAR model","level":4,"score":0.5269330739974976},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.42657631635665894},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.40963566303253174},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3796609044075012},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3754955530166626},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.369246244430542},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.19606584310531616},{"id":"https://openalex.org/C151406439","wikidata":"https://www.wikidata.org/wiki/Q186588","display_name":"Time series","level":2,"score":0.19028648734092712},{"id":"https://openalex.org/C24338571","wikidata":"https://www.wikidata.org/wiki/Q2566298","display_name":"Autoregressive integrated moving average","level":3,"score":0.18428444862365723},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1177/0081175018789441","doi":"https://doi.org/10.1177/0081175018789441","is_oa":false,"landing_page_url":"https://doi.org/10.1177/0081175018789441","pdf_url":null,"source":{"id":"https://openalex.org/S181883320","display_name":"Sociological Methodology","issn_l":"0081-1750","issn":["0081-1750","1467-9531"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["abdc-a","anvur-class-a","anvur-scientific","cwts-core","jufo-2","ki-jl-2","norway-2","poland-100","russia-white-list-1","vabb-shw"],"host_organization":"https://openalex.org/P4310320017","host_organization_name":"SAGE Publishing","host_organization_lineage":["https://openalex.org/P4310320017"],"host_organization_lineage_names":["SAGE Publishing"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Sociological Methodology","raw_type":"journal-article"},{"id":"pmid:31427831","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/31427831","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,"listed_in":[],"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":"Sociological methodology","raw_type":"Journal Article"},{"id":"pmh:oai:europepmc.org:5651711","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6699169","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6699169","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6699169","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Sociol Methodol","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:europepmc.org:5651711","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6699169","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"Text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G7282723123","display_name":"Carolina Population Center","funder_award_id":"P2CHD050924","funder_id":"https://openalex.org/F4320337611","funder_display_name":"Eunice Kennedy Shriver National Institute of Child Health and Human Development"}],"funders":[{"id":"https://openalex.org/F4320337611","display_name":"Eunice Kennedy Shriver National Institute of Child Health and Human Development","ror":"https://ror.org/04byxyr05"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W177281196","https://openalex.org/W1913957972","https://openalex.org/W1924064069","https://openalex.org/W1964579284","https://openalex.org/W1965984991","https://openalex.org/W1974955043","https://openalex.org/W1984524168","https://openalex.org/W1998225783","https://openalex.org/W2005142702","https://openalex.org/W2013763545","https://openalex.org/W2014543370","https://openalex.org/W2018201949","https://openalex.org/W2027325479","https://openalex.org/W2042042740","https://openalex.org/W2043837995","https://openalex.org/W2044394043","https://openalex.org/W2057933163","https://openalex.org/W2060283277","https://openalex.org/W2061223391","https://openalex.org/W2075371448","https://openalex.org/W2080134433","https://openalex.org/W2085652283","https://openalex.org/W2086312023","https://openalex.org/W2086452184","https://openalex.org/W2087383442","https://openalex.org/W2098705272","https://openalex.org/W2105840032","https://openalex.org/W2119880779","https://openalex.org/W2121297553","https://openalex.org/W2125511847","https://openalex.org/W2133051934","https://openalex.org/W2134971015","https://openalex.org/W2135220927","https://openalex.org/W2146855196","https://openalex.org/W2163825087","https://openalex.org/W2164085284","https://openalex.org/W2165193266","https://openalex.org/W2257183165","https://openalex.org/W2265936034","https://openalex.org/W2335391067","https://openalex.org/W2486260537","https://openalex.org/W2496673142","https://openalex.org/W2566737151","https://openalex.org/W2606120755","https://openalex.org/W2790298889","https://openalex.org/W4212792737","https://openalex.org/W4213428133","https://openalex.org/W4240549117","https://openalex.org/W4256238390","https://openalex.org/W4297782897","https://openalex.org/W4298091299","https://openalex.org/W4299927410"],"related_works":["https://openalex.org/W2027325479","https://openalex.org/W3138339359","https://openalex.org/W6962597726","https://openalex.org/W2057933163","https://openalex.org/W127305894","https://openalex.org/W2005142702","https://openalex.org/W2133051934","https://openalex.org/W7169876656","https://openalex.org/W6903675680","https://openalex.org/W2999681955"],"abstract_inverted_index":{"Autoregressive":[0],"latent":[1,8,91,109,118],"trajectory":[2,92],"(ALT)":[3],"models":[4,11,14,24,29,48,163],"combine":[5],"features":[6],"of":[7,22,54,60,73,88,107,145,186],"growth":[9,32,102,110,129,184],"curve":[10,111],"and":[12,70,139,171],"autoregressive":[13,90,169],"into":[15],"a":[16,100,104,150],"single":[17],"modeling":[18,183],"framework.":[19],"The":[20,95,113],"development":[21],"ALT":[23,47],"has":[25],"focused":[26],"primarily":[27],"on":[28,85],"with":[30,67],"linear":[31],"components,":[33],"but":[34],"some":[35,52],"social":[36],"processes":[37],"follow":[38],"nonlinear":[39,55,89,108,173],"trajectories.":[40,174],"Although":[41],"it":[42],"is":[43],"straightforward":[44],"to":[45,49,64,164],"extend":[46],"allow":[50,126],"for":[51,99,127,141],"forms":[53,87,144],"trajectories,":[56],"the":[57,71,142],"identification":[58],"status":[59],"such":[61],"models,":[62,69,120,124],"approaches":[63],"comparing":[65],"them":[66],"alternative":[68,162],"interpretation":[72],"parameters":[74],"have":[75],"not":[76],"been":[77],"systematically":[78],"assessed.":[79],"In":[80,175],"this":[81],"paper":[82],"we":[83,177],"focus":[84],"two":[86,143],"(NLALT)":[93],"models.":[94,112,147],"first":[96],"form":[97,106,115],"allows":[98],"quadratic":[101],"trajectory,":[103],"popular":[105],"second":[114],"derives":[116],"from":[117,160,167,188],"basis":[119],"or":[121],"freed":[122],"loading":[123],"that":[125,153,157],"arbitrary":[128],"processes.":[130],"We":[131,148],"discuss":[132],"details":[133],"concerning":[134],"parameterization,":[135],"model":[136],"identification,":[137],"estimation,":[138],"testing":[140],"NLALT":[146],"include":[149,178],"simulation":[151],"study":[152],"illustrates":[154],"potential":[155],"biases":[156],"may":[158],"arise":[159],"fitting":[161],"data":[165],"derived":[166],"an":[168,179],"process":[170],"individual-specific":[172],"addition,":[176],"extended":[180],"empirical":[181],"example":[182],"trajectories":[185],"weight":[187],"birth":[189],"through":[190],"age":[191],"2.":[192]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-11-03T10:50:19.383937","created_date":"2018-08-22T00:00:00"}
