A transition model for analyzing multivariate longitudinal data using Gaussian copula approach

  • Taban BaghfalakiEmail author
  • Mojtaba GanjaliEmail author
Original Paper


Longitudinal studies often involve multiple mixed response variables measured repeatedly over time. Although separate modeling of these multiple mixed response variables can be easily performed, they may lead to inefficient estimates and consequently, misleading inferences. For obtaining correct inference, one needs to model multiple mixed responses jointly. In this paper, we use copula models for defining a multivariate distribution for multiple mixed outcomes at each time point. Then, we use transition model for considering association between longitudinal measurements. Two simulation studies are performed for illustration of the proposed approach. The results of the simulation studies show that the use of the separate models instead of the joint modeling leads to inefficient parameter estimates. The proposed approach is also used for analyzing two real data sets. The first data set is a part of the British Household Panel Survey. In this data set, annual income and life satisfaction are considered as the continuous and the ordinal correlated longitudinal responses, respectively. The second data set is a longitudinal data about heart failure patients. This study is a treatment–control study, where the effect of a treatment is simultaneously investigated on readmission and referral to doctor as two binary associated longitudinal responses.


Copula function Joint modeling Longitudinal study Mixed data Ordinal regression Transition model 



The authors are grateful to School of Biological Sciences at IPM for their supports. This research is supported in part by a grant (BS-1396-02-01) from the Institute for Research in Fundamental Sciences (IPM), Tehran, Iran.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Statistics, Faculty of Mathematical SciencesTarbiat Modares UniversityTehranIran
  2. 2.Department of Statistics, Faculty of Mathematical SciencesShahid Beheshti UniversityTehranIran
  3. 3.School of Biological ScienceInstitute for Research in Fundamental Sciences (IPM)TehranIran

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