Abstract
The aim of the work is to propose a new flexible way of modeling the dependence between the components of non-normal multivariate longitudinal-data by using the copula approach. The presence of longitudinal data is increasing in the scientific areas where several variables aremeasured over a sample of statistical units at different times, showing two types of dependence: between variables and across time. We propose to model jointly the dependence structure between the responses and the temporal structure of each processes by pair copula contruction (PCC). The use of the copula allows the relaxation of the assumption of multinormality that is typical of the usual model for multivariate longitudinal data. The use of PCC allows us to overcome the problem of the multivariate copulae used in the literature which suffer from rather inflexible structures in high dimension. The result is a newextremly flexible model for multivariate longitudinal data, which overcomes the problem of modeling simultaneous dependence between two ormore non-normal responses over time. The explanation of the methodology is accompanied by an example.