Modelling the dependence in multivariate longitudinal data by pair copula decomposition

A new flexible way of modeling the dependence between the components of non-normal multivariate longitudinal-data is proposed by using the copula approach. The presence of longitudinal data is increasing in the scientific areas where several variables are measured over a sample of statistical units at different times, showing two types of dependence: between variables and across time. In order to account both type of dependence the proposed model considers two levels of analysis. First given a specific time, we model the relations of variables using copula. The use of the copula allows us to relax the assumption of normality. In the second level, each longitudinal series, corresponding to a given response over time, is modelled separately using a pair copula decomposition to relate the distributions of the variables describing the observation taken in different times. The use of the pair copula decomposition 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 new extreme flexible multivariate longitudinal model, which overcomes the problem of modelling simultaneous dependence between two or more non-normal time-series.