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Furthermore, their incorporation of normal random effects into beta\u2010binomial models has been done at the sacrifice of certain computational convenience and clear interpretation with beta\u2010binomial models. In this paper, we introduce a new model that incorporates subject\u2010specific and serially correlated time\u2010specific distribution\u2010free random effects on the unit interval into logistic regression multiplicatively with fixed effects. This new multiplicative model facilitates the interpretation of random effects on the unit interval as risk modifiers. This multiplicative model setup also eases the model derivation and random effects prediction. A quasi\u2010likelihood approach has been developed in the estimation of our model. Our results are robust against random effects distributions. Our method is illustrated through the analysis of multiple sclerosis trial\u00a0data.<\/jats:p>","DOI":"10.1002\/bimj.70078","type":"journal-article","created":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T13:05:26Z","timestamp":1759064726000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A New Logistic Model with Subject\u2010Specific and Serially Correlated Time\u2010Specific Distribution\u2010Free Random Effects on the Unit Interval for Longitudinal Binary Data"],"prefix":"10.1002","volume":"67","author":[{"given":"Lulu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics Yunnan Normal University  Kunming China"},{"name":"Department of Mathematics and Statistics University of New Brunswick  Fredericton Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5243-5426","authenticated-orcid":false,"given":"Renjun","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics University of New Brunswick  Fredericton Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4491-9559","authenticated-orcid":false,"given":"Guohua","family":"Yan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics University of New Brunswick  Fredericton Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1593-5864","authenticated-orcid":false,"given":"Xifen","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Mathematics Yunnan Normal University  Kunming China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,9,28]]},"reference":[{"key":"e_1_2_10_2_1","doi-asserted-by":"publisher","DOI":"10.1002\/sim.9005"},{"key":"e_1_2_10_3_1","unstructured":"Hofert M. 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