{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T05:00:11Z","timestamp":1789534811356,"version":"build-2803163510"},"reference-count":19,"publisher":"Wiley","issue":"19","license":[{"start":{"date-parts":[[2013,2,24]],"date-time":"2013-02-24T00:00:00Z","timestamp":1361664000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2013,2,24]],"date-time":"2013-02-24T00:00:00Z","timestamp":1361664000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"},{"start":{"date-parts":[[2013,2,24]],"date-time":"2013-02-24T00:00:00Z","timestamp":1361664000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["wiley.com"],"crossmark-restriction":true},"short-container-title":["Statistics in Medicine"],"published-print":{"date-parts":[[2013,8,30]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Time index\u2010ordered random variables are said to be antedependent (AD) of order (<jats:italic>p<\/jats:italic><jats:sub>1<\/jats:sub>,<jats:italic>p<\/jats:italic><jats:sub>2<\/jats:sub>,\u2009\u2026\u2009,<jats:italic>p<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) if the<jats:italic>k<\/jats:italic>th variable, conditioned on the<jats:italic>p<\/jats:italic><jats:sub><jats:italic>k<\/jats:italic><\/jats:sub>immediately preceding variables, is independent of all further preceding variables. Inferential methods associated with AD models are well developed for continuous (primarily normal) longitudinal data, but not for categorical longitudinal data. In this article, we develop likelihood\u2010based inferential procedures for unstructured AD models for categorical longitudinal data. Specifically, we derive maximum likelihood estimators (MLEs) of model parameters; penalized likelihood criteria and likelihood ratio tests for determining the order of antedependence; and likelihood ratio tests for homogeneity across groups, time invariance of transition probabilities, and strict stationarity. We give closed\u2010form expressions for MLEs and test statistics, which allow for the possibility of empty cells and monotone missing data, for all cases save strict stationarity. For data with an arbitrary missingness pattern, we derive an efficient restricted expectation\u2013maximization algorithm for obtaining MLEs. We evaluate the performance of the tests by simulation. We apply the methods to longitudinal studies of toenail infection severity (measured on a binary scale) and Alzheimer's disease severity (measured on an ordinal scale). The analysis of the toenail infection severity data reveals interesting nonstationary behavior of the transition probabilities and indicates that an unstructured first\u2010order AD model is superior to stationary and other structured first\u2010order AD models that have previously been fit to these data. The analysis of the Alzheimer's severity data indicates that the antedependence is second order with time\u2010invariant transition probabilities, suggesting the use of a second\u2010order autoregressive cumulative logit model. Copyright \u00a9 2013 John Wiley &amp; Sons, Ltd.<\/jats:p>","DOI":"10.1002\/sim.5763","type":"journal-article","created":{"date-parts":[[2013,2,25]],"date-time":"2013-02-25T03:36:40Z","timestamp":1361763400000},"page":"3274-3289","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Antedependence models for\u2009nonstationary categorical longitudinal data with ignorable missingness: likelihood\u2010based inference"],"prefix":"10.1002","volume":"32","author":[{"given":"Yunlong","family":"Xie","sequence":"first","affiliation":[{"name":"Biostatistics and Bioinformatics Branch, Division of Epidemiology Statistics and Prevention Research Eunice Kennedy Shriver National Institute of Child Health and Human Development National Institutes of Health Bethesda MD 20892 U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dale L.","family":"Zimmerman","sequence":"additional","affiliation":[{"name":"Department of Statistics and Actuarial Science 241 Schaeffer Hall, University of Iowa Iowa City IA 52242 U.S.A."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2013,2,24]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198524847.001.0001","volume-title":"Analysis of Longitudinal Data","author":"Diggle PJ","year":"2002"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704724"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1080\/03610929408831410"},{"key":"e_1_2_11_5_1","volume-title":"Antedependence Models for Longitudinal Data","author":"Zimmerman DL","year":"2010"},{"key":"e_1_2_11_6_1","volume-title":"Analysis of Binary Data","author":"Cox DR","year":"1989"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2531732"},{"key":"e_1_2_11_8_1","volume-title":"Models for Discrete Longitudinal Data","author":"Molenberghs G","year":"2005"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1042727943"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/81.4.767"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1214\/ss\/1009212671"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.0006-341X.2002.00342.x"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1541-0420.2007.00800.x"},{"key":"e_1_2_11_14_1","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177707039"},{"key":"e_1_2_11_15_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1079120140"},{"key":"e_1_2_11_16_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1995.10476564"},{"key":"e_1_2_11_17_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781439821862"},{"key":"e_1_2_11_18_1","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/43.3-4.295"},{"key":"e_1_2_11_19_1","doi-asserted-by":"publisher","DOI":"10.1002\/0471249688"},{"key":"e_1_2_11_20_1","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1018031204"}],"container-title":["Statistics in Medicine"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.5763","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fsim.5763","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/sim.5763","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,6]],"date-time":"2024-05-06T12:07:34Z","timestamp":1714997254000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/sim.5763"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,24]]},"references-count":19,"journal-issue":{"issue":"19","published-print":{"date-parts":[[2013,8,30]]}},"alternative-id":["10.1002\/sim.5763"],"URL":"https:\/\/doi.org\/10.1002\/sim.5763","archive":["Portico"],"relation":{},"ISSN":["0277-6715","1097-0258"],"issn-type":[{"value":"0277-6715","type":"print"},{"value":"1097-0258","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,2,24]]}}}