Modeling Multivariate Longitudinal Data Using Vine Pair Copula Constructions

In some medical studies, we may have several measurements on each patient. Sometimes these longitudinal data may be measured for several response variables, in this case, although the responses can be modeled separately, such an approach reduces the power and efficiency in estimating the effects of auxiliary variables on the response variable. In the analysis of such data, in addition to the analysis of the dependence between repeated measures related to each of the response variables, the dependence between the responses should also be considered. Among the methods used in recent years to model multivariate data is the copulafunction. One of the most important advantages of using the copula function compared to the longitudinal multivariate modeling of the data in the classic way is that, in addition to the normal distribution, any other distribution other than the normal can be considered as marginal distributions. Also, marginal distributions can even have different distributions. In situations where the data have a multivariate structure, one of the ways to form multivariate distributions is to use vine pair-copula function. In this study, we form a multivariate longitudinal structure by using the vine pair copula functions and compare these models with the model obtained from the fitting of the multivariate normal copula function. Then we will introduce the best model using the Akaike information criterion and at the end we will use the presented model on the data of the estimation of the effect of nutrition on growth.