{"id":"https://openalex.org/W2063055671","doi":"https://doi.org/10.1080/03610911003778085","title":"An Appraisal of Methods for the Analysis of Longitudinal Ordinal Response Data with Random Dropout Using a Nonhomogeneous Markov Model","display_name":"An Appraisal of Methods for the Analysis of Longitudinal Ordinal Response Data with Random Dropout Using a Nonhomogeneous Markov Model","publication_year":2010,"publication_date":"2010-04-30","ids":{"openalex":"https://openalex.org/W2063055671","doi":"https://doi.org/10.1080/03610911003778085","mag":"2063055671"},"language":"en","primary_location":{"id":"doi:10.1080/03610911003778085","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610911003778085","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/A5064414401","display_name":"Zahra Rezaei Ghahroodi","orcid":"https://orcid.org/0000-0002-9138-8535"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Z. Rezaei Ghahroodi","raw_affiliation_strings":["Statistical Research and Training Center","Statistical Research and Training Center , Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Statistical Research and Training Center","institution_ids":[]},{"raw_affiliation_string":"Statistical Research and Training Center , Tehran, Iran","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026928158","display_name":"Mojtaba Ganjali","orcid":"https://orcid.org/0000-0002-8574-1750"},"institutions":[{"id":"https://openalex.org/I48379061","display_name":"Shahid Beheshti University","ror":"https://ror.org/0091vmj44","country_code":"IR","type":"education","lineage":["https://openalex.org/I48379061"]}],"countries":["IR"],"is_corresponding":true,"raw_author_name":"M. Ganjali","raw_affiliation_strings":["Shahid Beheshti University, G.C","Department of Statistics, Faculty of Mathematical Science , Shahid Beheshti University, G.C. , Tehran, Iran"],"affiliations":[{"raw_affiliation_string":"Shahid Beheshti University, G.C","institution_ids":["https://openalex.org/I48379061"]},{"raw_affiliation_string":"Department of Statistics, Faculty of Mathematical Science , Shahid Beheshti University, G.C. , Tehran, Iran","institution_ids":["https://openalex.org/I48379061"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018672202","display_name":"Hamidreza Navvabpour","orcid":null},"institutions":[{"id":"https://openalex.org/I200432940","display_name":"Allameh Tabataba'i University","ror":"https://ror.org/02cc4gc68","country_code":"IR","type":"education","lineage":["https://openalex.org/I200432940"]}],"countries":["IR"],"is_corresponding":false,"raw_author_name":"H. Navvabpour","raw_affiliation_strings":["Allameh Tabataba'i University","Department of Statistics, Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran#TAB#"],"affiliations":[{"raw_affiliation_string":"Allameh Tabataba'i University","institution_ids":["https://openalex.org/I200432940"]},{"raw_affiliation_string":"Department of Statistics, Faculty of Economics, Allameh Tabataba'i University, Tehran, Iran#TAB#","institution_ids":["https://openalex.org/I200432940"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010845260","display_name":"Damon Berridge","orcid":"https://orcid.org/0000-0002-5442-6686"},"institutions":[{"id":"https://openalex.org/I67415387","display_name":"Lancaster University","ror":"https://ror.org/04f2nsd36","country_code":"GB","type":"education","lineage":["https://openalex.org/I67415387"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"D. Berridge","raw_affiliation_strings":["Lancaster University","Department of Mathematics and Statistics, Lancaster University, Lancaster, UK;"],"affiliations":[{"raw_affiliation_string":"Lancaster University","institution_ids":["https://openalex.org/I67415387"]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Lancaster University, Lancaster, UK;","institution_ids":["https://openalex.org/I67415387"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5026928158"],"corresponding_institution_ids":["https://openalex.org/I48379061"],"apc_list":null,"apc_paid":null,"fwci":0.2815,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.62020187,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":"5","first_page":"1027","last_page":"1048"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10243","display_name":"Statistical Methods and Bayesian Inference","score":0.9998000264167786,"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":0.9998000264167786,"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/T11235","display_name":"Statistical Methods in Clinical Trials","score":0.9980999827384949,"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/T10136","display_name":"Statistical Methods and Inference","score":0.9972000122070312,"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/dropout","display_name":"Dropout (neural networks)","score":0.7262551784515381},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.6793243288993835},{"id":"https://openalex.org/keywords/ordinal-data","display_name":"Ordinal data","score":0.61337810754776},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5751014947891235},{"id":"https://openalex.org/keywords/markov-chain","display_name":"Markov chain","score":0.5627280473709106},{"id":"https://openalex.org/keywords/random-effects-model","display_name":"Random effects model","score":0.5461845993995667},{"id":"https://openalex.org/keywords/longitudinal-data","display_name":"Longitudinal data","score":0.4617822766304016},{"id":"https://openalex.org/keywords/markov-model","display_name":"Markov model","score":0.4421805739402771},{"id":"https://openalex.org/keywords/data-set","display_name":"Data set","score":0.440470427274704},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.36620408296585083},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34708335995674133},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.19592848420143127},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.15639695525169373},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.06526586413383484}],"concepts":[{"id":"https://openalex.org/C2776145597","wikidata":"https://www.wikidata.org/wiki/Q25339462","display_name":"Dropout (neural networks)","level":2,"score":0.7262551784515381},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.6793243288993835},{"id":"https://openalex.org/C85461838","wikidata":"https://www.wikidata.org/wiki/Q7100785","display_name":"Ordinal data","level":2,"score":0.61337810754776},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5751014947891235},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.5627280473709106},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.5461845993995667},{"id":"https://openalex.org/C3020672099","wikidata":"https://www.wikidata.org/wiki/Q857354","display_name":"Longitudinal data","level":2,"score":0.4617822766304016},{"id":"https://openalex.org/C163836022","wikidata":"https://www.wikidata.org/wiki/Q6771326","display_name":"Markov model","level":3,"score":0.4421805739402771},{"id":"https://openalex.org/C58489278","wikidata":"https://www.wikidata.org/wiki/Q1172284","display_name":"Data set","level":2,"score":0.440470427274704},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.36620408296585083},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34708335995674133},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.19592848420143127},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.15639695525169373},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06526586413383484},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C95190672","wikidata":"https://www.wikidata.org/wiki/Q815382","display_name":"Meta-analysis","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610911003778085","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610911003778085","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":[{"id":"https://openalex.org/G3324899703","display_name":null,"funder_award_id":"ES/F032242/1","funder_id":"https://openalex.org/F4320334630","funder_display_name":"Economic and Social Research Council"}],"funders":[{"id":"https://openalex.org/F4320334630","display_name":"Economic and Social Research Council","ror":"https://ror.org/03n0ht308"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W214995755","https://openalex.org/W618810304","https://openalex.org/W1540939704","https://openalex.org/W1600582725","https://openalex.org/W1895131631","https://openalex.org/W1971950880","https://openalex.org/W1985176986","https://openalex.org/W1988692535","https://openalex.org/W1990681166","https://openalex.org/W1992570540","https://openalex.org/W1994385600","https://openalex.org/W2004887252","https://openalex.org/W2017599218","https://openalex.org/W2022772618","https://openalex.org/W2024085858","https://openalex.org/W2037245526","https://openalex.org/W2038173886","https://openalex.org/W2039575469","https://openalex.org/W2039892910","https://openalex.org/W2042803051","https://openalex.org/W2044758663","https://openalex.org/W2049320016","https://openalex.org/W2050762021","https://openalex.org/W2052074824","https://openalex.org/W2054014518","https://openalex.org/W2054140640","https://openalex.org/W2054331551","https://openalex.org/W2054353235","https://openalex.org/W2056859449","https://openalex.org/W2059166063","https://openalex.org/W2068502909","https://openalex.org/W2069751717","https://openalex.org/W2070487393","https://openalex.org/W2073453589","https://openalex.org/W2074673068","https://openalex.org/W2076983043","https://openalex.org/W2085667778","https://openalex.org/W2087686387","https://openalex.org/W2089698443","https://openalex.org/W2096227368","https://openalex.org/W2098906202","https://openalex.org/W2103672914","https://openalex.org/W2116739230","https://openalex.org/W2118502261","https://openalex.org/W2139718926","https://openalex.org/W2143867469","https://openalex.org/W2145816995","https://openalex.org/W2148441587","https://openalex.org/W2149860264","https://openalex.org/W2157649245","https://openalex.org/W2168666402","https://openalex.org/W2171653202","https://openalex.org/W2284967628","https://openalex.org/W2318032547","https://openalex.org/W2478445791","https://openalex.org/W2480680997","https://openalex.org/W2513881572","https://openalex.org/W4230779573","https://openalex.org/W4231032363","https://openalex.org/W4238109618","https://openalex.org/W4242347361","https://openalex.org/W4242611672","https://openalex.org/W4243722435","https://openalex.org/W4249593981","https://openalex.org/W4251419164","https://openalex.org/W4301159042","https://openalex.org/W4388319941"],"related_works":["https://openalex.org/W2150929603","https://openalex.org/W2372409582","https://openalex.org/W2052180015","https://openalex.org/W3179562413","https://openalex.org/W1581190534","https://openalex.org/W2160852089","https://openalex.org/W3124407991","https://openalex.org/W2040713875","https://openalex.org/W31670354","https://openalex.org/W2019370408"],"abstract_inverted_index":{"Abstract":[0],"There":[1],"are":[2,73,95,119,128,137,146,154],"many":[3],"methods":[4,83,94],"for":[5],"analyzing":[6],"longitudinal":[7,68,109],"ordinal":[8,48],"response":[9,39,43],"data":[10,101],"with":[11,70,122,131,140],"random":[12,71],"dropout.":[13],"These":[14,92],"include":[15],"maximum":[16],"likelihood":[17,51],"(ML),":[18],"weighted":[19],"estimating":[20,111],"equations":[21],"(WEEs),":[22],"and":[23,81,89],"multiple":[24],"imputations":[25],"(MI).":[26],"In":[27],"this":[28],"article,":[29],"using":[30],"a":[31,66,98],"Markov":[32,106],"model":[33],"where":[34],"the":[35,41,50,56],"effect":[36],"of":[37,58,78,86],"previous":[38],"on":[40],"current":[42],"is":[44,52],"investigated":[45],"as":[46],"an":[47],"variable,":[49],"partitioned":[53],"to":[54,64,75,97],"simplify":[55],"use":[57],"existing":[59],"software.":[60],"Simulated":[61],"data,":[62],"generated":[63],"present":[65],"three-period":[67],"study":[69],"dropout,":[72],"used":[74],"compare":[76],"performance":[77],"ML,":[79],"WEE,":[80],"MI":[82],"in":[84],"terms":[85],"standardized":[87,123,132,141],"bias":[88,124,133,142],"coverage":[90,147],"probabilities.":[91],"estimation":[93],"applied":[96],"real":[99],"medical":[100],"set.":[102],"Keywords:":[103],"Multiple":[104],"imputationNonhomogeneous":[105],"modelRandom":[107],"dropoutShort-period":[108],"dataWeighted":[110],"equationsMathematics":[112],"Subject":[113],"Classification:":[114],"62P10":[115],"Notes":[116],"Bold":[117,126,135,144,152],"numbers":[118,127,136,145,153],"estimated":[120,129,138],"parameters":[121,130,139],">0.4.":[125,134,143],"probabilities":[148],"less":[149],"than":[150],"0.90.":[151],"significant":[155],"at":[156],"5%":[157],"level.":[158]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-01-22T23:29:09.771500","created_date":"2025-10-10T00:00:00"}