{"id":"https://openalex.org/W1580162914","doi":"https://doi.org/10.1080/03610910903480800","title":"Estimating Transition Probabilities for Ignorable Intermittent Missing Data in a Discrete-Time Markov Chain","display_name":"Estimating Transition Probabilities for Ignorable Intermittent Missing Data in a Discrete-Time Markov Chain","publication_year":2010,"publication_date":"2010-01-11","ids":{"openalex":"https://openalex.org/W1580162914","doi":"https://doi.org/10.1080/03610910903480800","mag":"1580162914"},"language":"en","primary_location":{"id":"doi:10.1080/03610910903480800","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910903480800","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081458605","display_name":"Hung\u2010Wen Yeh","orcid":"https://orcid.org/0000-0002-9904-3275"},"institutions":[{"id":"https://openalex.org/I4210128618","display_name":"University of Kansas Medical Center","ror":"https://ror.org/036c9yv20","country_code":"US","type":"funder","lineage":["https://openalex.org/I4210128618"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Hung-Wen Yeh","raw_affiliation_strings":["a Department of Biostatistics , University of Kansas Medical Center , Kansas City, Kansas, USA","Department of Biostatistics, University of Kansas Medical Center, Kansas City, Kansas, USA,"],"affiliations":[{"raw_affiliation_string":"a Department of Biostatistics , University of Kansas Medical Center , Kansas City, Kansas, USA","institution_ids":["https://openalex.org/I4210128618"]},{"raw_affiliation_string":"Department of Biostatistics, University of Kansas Medical Center, Kansas City, Kansas, USA,","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5022469672","display_name":"Wenyaw Chan","orcid":"https://orcid.org/0000-0003-3329-5282"},"institutions":[{"id":"https://openalex.org/I919571938","display_name":"The University of Texas Health Science Center at Houston","ror":"https://ror.org/03gds6c39","country_code":"US","type":"education","lineage":["https://openalex.org/I919571938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wenyaw Chan","raw_affiliation_strings":["b Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA","Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA"],"affiliations":[{"raw_affiliation_string":"b Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA","institution_ids":["https://openalex.org/I919571938"]},{"raw_affiliation_string":"Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA","institution_ids":["https://openalex.org/I919571938"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088985802","display_name":"Elaine Symanski","orcid":"https://orcid.org/0000-0002-9073-8898"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]},{"id":"https://openalex.org/I919571938","display_name":"The University of Texas Health Science Center at Houston","ror":"https://ror.org/03gds6c39","country_code":"US","type":"education","lineage":["https://openalex.org/I919571938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Elaine Symanski","raw_affiliation_strings":["c Division of Epidemiology and Disease Control , The University of Texas School of Public Health , Houston, Texas, USA","Division of Epidemiology and Disease Control , The University of Texas School of Public Health , Houston , Texas , USA"],"affiliations":[{"raw_affiliation_string":"c Division of Epidemiology and Disease Control , The University of Texas School of Public Health , Houston, Texas, USA","institution_ids":["https://openalex.org/I919571938"]},{"raw_affiliation_string":"Division of Epidemiology and Disease Control , The University of Texas School of Public Health , Houston , Texas , USA","institution_ids":["https://openalex.org/I86519309"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042299275","display_name":"Barry R. Davis","orcid":"https://orcid.org/0000-0002-6943-5673"},"institutions":[{"id":"https://openalex.org/I919571938","display_name":"The University of Texas Health Science Center at Houston","ror":"https://ror.org/03gds6c39","country_code":"US","type":"education","lineage":["https://openalex.org/I919571938"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Barry R. Davis","raw_affiliation_strings":["b Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA","Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA"],"affiliations":[{"raw_affiliation_string":"b Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA","institution_ids":["https://openalex.org/I919571938"]},{"raw_affiliation_string":"Division of Biostatistics , The University of Texas School of Public Health , Houston, Texas, USA","institution_ids":["https://openalex.org/I919571938"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5081458605"],"corresponding_institution_ids":["https://openalex.org/I4210128618"],"apc_list":null,"apc_paid":null,"fwci":1.126,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.7811592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"39","issue":"2","first_page":"433","last_page":"448"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9968000054359436,"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"}},"topics":[{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian 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/T13283","display_name":"Mental Health Research Topics","score":0.9950000047683716,"subfield":{"id":"https://openalex.org/subfields/3205","display_name":"Experimental and Cognitive Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11235","display_name":"Statistical Methods in Clinical Trials","score":0.9868999719619751,"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/missing-data","display_name":"Missing data","score":0.7623134851455688},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.7018102407455444},{"id":"https://openalex.org/keywords/expectation\u2013maximization-algorithm","display_name":"Expectation\u2013maximization algorithm","score":0.5952699184417725},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.5038830637931824},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4872792959213257},{"id":"https://openalex.org/keywords/imputation","display_name":"Imputation (statistics)","score":0.48016613721847534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4657156467437744},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4401933550834656},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.41829031705856323},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3437133729457855},{"id":"https://openalex.org/keywords/maximum-likelihood","display_name":"Maximum likelihood","score":0.2667391002178192}],"concepts":[{"id":"https://openalex.org/C9357733","wikidata":"https://www.wikidata.org/wiki/Q6878417","display_name":"Missing data","level":2,"score":0.7623134851455688},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.7018102407455444},{"id":"https://openalex.org/C182081679","wikidata":"https://www.wikidata.org/wiki/Q1275153","display_name":"Expectation\u2013maximization algorithm","level":3,"score":0.5952699184417725},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.5038830637931824},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4872792959213257},{"id":"https://openalex.org/C58041806","wikidata":"https://www.wikidata.org/wiki/Q1660484","display_name":"Imputation (statistics)","level":3,"score":0.48016613721847534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4657156467437744},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4401933550834656},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.41829031705856323},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3437133729457855},{"id":"https://openalex.org/C49781872","wikidata":"https://www.wikidata.org/wiki/Q1045555","display_name":"Maximum likelihood","level":2,"score":0.2667391002178192}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610910903480800","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610910903480800","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332697","display_name":"University of Illinois at Chicago","ror":"https://ror.org/02mpq6x41"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1984514250","https://openalex.org/W2017070295","https://openalex.org/W2020129240","https://openalex.org/W2036319502","https://openalex.org/W2044758663","https://openalex.org/W2049633694","https://openalex.org/W2049663477","https://openalex.org/W2075359038","https://openalex.org/W2089834667","https://openalex.org/W2156746747","https://openalex.org/W4232217265","https://openalex.org/W6721667826"],"related_works":["https://openalex.org/W2181530120","https://openalex.org/W4211215373","https://openalex.org/W2024529227","https://openalex.org/W2055961818","https://openalex.org/W1574575415","https://openalex.org/W3144172081","https://openalex.org/W3179858851","https://openalex.org/W3028371478","https://openalex.org/W2081476516","https://openalex.org/W2581984549"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"article":[2],"considers":[3],"a":[4,27,39,49,86],"discrete-time":[5],"Markov":[6],"chain":[7],"for":[8,130,211],"modeling":[9],"transition":[10,157],"probabilities":[11,158],"when":[12],"multiple":[13],"successive":[14],"observations":[15],"are":[16],"missing":[17,110,113,118,396,415],"at":[18,115,119,209],"random":[19,116],"between":[20,398,410],"two":[21,399,411],"observed":[22,35,65,400],"outcomes":[23],"using":[24,33],"three":[25,106],"methods:":[26],"na\\\"\u0131ve":[28,150],"analog":[29],"of":[30,59,100,112,155,205,207,240,245,279,284,318,323,357,362,395],"complete-case":[31],"analysis":[32],"the":[34,52,60,64,70,76,80,96,101,105,124,149,156,169,178,216,230,238,241,246,277,280,285,316,319,324,355,358,363,407],"one-step":[36,408],"transitions":[37,409],"alone,":[38],"non":[40],"data-augmentation":[41,50,137],"method":[42,151,167],"(NL)":[43],"by":[44,69],"solving":[45],"nonlinear":[46],"equations,":[47],"and":[48,75,98,117,138,143,147,168,227],"method,":[51],"Expectation-Maximization":[53],"(EM)":[54],"algorithm.":[55],"The":[56,165],"explicit":[57],"form":[58],"conditional":[61,181],"log-likelihood":[62],"given":[63],"information":[66],"as":[67],"required":[68],"E":[71],"step":[72,82],"is":[73,83],"provided,":[74],"iterative":[77],"formula":[78],"in":[79,85,104,153,172,262,265,301,304,340,343,379,382,417],"M":[81],"expressed":[84],"closed":[87],"form.":[88],"An":[89],"empirical":[90,243,282,321,360],"study":[91],"was":[92,128,133],"performed":[93],"to":[94,186,214,222,259,298,337,376,406],"examine":[95],"accuracy":[97],"precision":[99],"estimates":[102,154,261,300,339,378],"obtained":[103,236,250,270,275,289,309,314,328,348,353,367,387],"methods":[107,140],"under":[108],"ignorable":[109],"mechanisms":[111],"completely":[114],"random.":[120],"A":[121],"dataset":[122],"from":[123,237,251,271,276,290,310,315,329,349,354,368,388],"mental":[125],"health":[126],"arena":[127],"used":[129],"illustration.":[131],"It":[132],"found":[134],"that":[135,148],"both":[136],"nonaugmentation":[139],"provide":[141,174],"accurate":[142],"precise":[144],"point":[145],"estimation,":[146],"resulted":[152],"with":[159],"similar":[160,175],"bias":[161],"but":[162],"larger":[163],"MSE.":[164],"NL":[166],"EM":[170,191],"algorithm":[171],"general":[173],"results":[176],"whereas":[177],"latter":[179],"provides":[180],"expected":[182],"row":[183],"margins":[184],"leading":[185],"smaller":[187],"standard":[188],"errors.":[189],"Keywords:":[190],"algorithmIncomplete":[192],"dataLongitudinalMarkov":[193],"chainMissing":[194],"valuesMathematics":[195],"Subject":[196],"Classification:":[197],"62-XX62Mxx":[198],"Acknowledgments":[199],"We":[200],"thank":[201],"Dr.":[202],"Donald":[203],"Hedeker":[204],"University":[206],"Illinois":[208],"Chicago":[210],"his":[212],"permission":[213],"use":[215],"schizophrenia":[217],"dataset.":[218],"Appreciation":[219],"also":[220],"goes":[221],"Drs.":[223],"John":[224],"M.":[225],"Davis":[226],"Nina":[228],"Schooler,":[229],"original":[231],"data":[232],"owners.":[233],"Notes":[234],"SE1:":[235,274,313,352],"SD":[239,278,317,356],"1,000-run":[242,281,320,359],"distribution":[244,283,322,361],"parameter.":[247,286,325,364],"SE2:":[248,287,326,365],"SE":[249,288,327,366],"Eq.":[252,291,330,369],"(2).":[253,292,331,370],"\u2020based":[254,293,332,371],"on":[255,294,333,372],"968":[256],"runs":[257,296,335,374],"due":[258,297,336,375],"negative-value":[260,299,338,377],"PROC":[263,302,341,380],"NLP":[264,303,342,381],"32":[266],"runs.":[267,306,345,384],"\u2021Cmpl":[268,307,346,385],"=estimates":[269,308,347,386],"complete":[272,311,350,389],"data.":[273,312,351,390],"902":[295],"98":[305],"812":[334],"188":[344],"906":[373],"94":[383],"1":[391],"m":[392,402],"=":[393,403],"Number":[394],"values":[397],"ones.":[401],"0":[404],"refers":[405],"states":[412],"without":[413],"any":[414],"value":[416],"between;":[418],"2S":[419],"=severe;":[420],"3Mo":[421],"=moderate;":[422],"4Mi":[423],"=mild;":[424],"5":[425],"N":[426],"=normal;":[427],"6Sum":[428],"=row":[429],"margins.":[430],"\u2020Extremely":[431,436,441],"small":[432,437,442],"values.":[433,438,443],"\u2021Not":[434,439],"available.":[435,440],"\u2217Significant":[444],"difference.":[445]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}