{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,15]],"date-time":"2025-07-15T03:48:00Z","timestamp":1752551280823,"version":"3.40.5"},"reference-count":36,"publisher":"Wiley","license":[{"start":{"date-parts":[[2021,3,3]],"date-time":"2021-03-03T00:00:00Z","timestamp":1614729600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2021,3,3]]},"abstract":"<jats:p>Associated longitudinal response variables are faced with variations caused by repeated measurements over time along with the association between the responses. To model a longitudinal ordinal outcome using generalized linear mixed models, integrating over a normally distributed random intercept in the proportional odds ordinal logistic regression does not yield a closed form. In this paper, we combined a longitudinal count and an ordinal response variable with Bridge distribution for the random intercept in the ordinal logistic regression submodel. We compared the results to that of a normal distribution. The two associated response variables are combined using correlated random intercepts. The random intercept in the count outcome submodel follows a normal distribution. The random intercept in the ordinal outcome submodel follows Bridge distribution. The estimations were carried out using a likelihood-based approach in direct and conditional joint modelling approaches. To illustrate the performance of the model, a simulation study was conducted. Based on the simulation results, assuming a Bridge distribution for the random intercept of ordinal logistic regression results in accurate estimation even if the random intercept is normally distributed. Moreover, considering the association between longitudinal count and ordinal responses resulted in estimation with lower standard error in comparison to univariate analysis. In addition to the same interpretation for the parameter in marginal and conditional estimates thanks to the assumption of a Bridge distribution for the random intercept of ordinal logistic regression, more efficient estimates were found compared to that of normal distribution.<\/jats:p>","DOI":"10.1155\/2021\/5521881","type":"journal-article","created":{"date-parts":[[2021,3,4]],"date-time":"2021-03-04T01:50:16Z","timestamp":1614822616000},"page":"1-13","source":"Crossref","is-referenced-by-count":3,"title":["Longitudinal Joint Modelling of Ordinal and Overdispersed Count Outcomes: A Bridge Distribution for the Ordinal Random Intercept"],"prefix":"10.1155","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8675-0045","authenticated-orcid":true,"given":"Payam","family":"Amini","sequence":"first","affiliation":[{"name":"Department of Biostatistics and Epidemiology, School of Public Health, Ahvaz Jundishapur University of Medical Sciences, Ahvaz, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3803-3663","authenticated-orcid":true,"given":"Abbas","family":"Moghimbeigi","sequence":"additional","affiliation":[{"name":"Department of Biostatistics and Epidemiology, School of Health, Research Center for Health, Safety and Environment, Alborz University of Medical Sciences, Karaj, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7791-8122","authenticated-orcid":true,"given":"Farid","family":"Zayeri","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, Member of Proteomics Research Center, School of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4378-3143","authenticated-orcid":true,"given":"Leili","family":"Tapak","sequence":"additional","affiliation":[{"name":"Department of Biostatistics, School of Public Health, Hamadan University of Medical Science, Hamadan, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5794-3876","authenticated-orcid":true,"given":"Saman","family":"Maroufizadeh","sequence":"additional","affiliation":[{"name":"School of Nursing and Midwifery, Guilan University of Medical Sciences, Rasht, Iran"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8430-7576","authenticated-orcid":true,"given":"Geert","family":"Verbeke","sequence":"additional","affiliation":[{"name":"Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Katholieke Universiteit Leuven, B-3000 Leuven, Belgium"},{"name":"Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Universiteit Hasselt, B-3590 Diepenbeek, Belgium"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","DOI":"10.1201\/9781420011579","volume-title":"Longitudinal Data Analysis","author":"G. 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