Modelling the Dependence in Multivariate Longitudinal Data by Pair Copula Decomposition
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
- PDF / 190,291 Bytes
- 8 Pages / 439.37 x 666.142 pts Page_size
- 28 Downloads / 199 Views
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 are measured 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 new extremly flexible model for multivariate longitudinal data, which overcomes the problem of modeling simultaneous dependence between two or more non-normal responses over time. The explanation of the methodology is accompanied by an example.
1 Introduction Longitudinal data show an increasing occurrence in many scientific research areas where several response variables are measured with reference to a sample of statistical units at different times. The advantage of this study is that it can provide information about subject change, by collecting repeated measurements over time. In this type of data, there are two types of dependence: between variables and over time. The multivariate longitudinal models usually considered in the literature are based on the normality assumption (e.g. [8, 9]). Unfortunately, the empirical evidence shows that normality is certainly not a rule in practice. When the responses are not normal M. Nai Ruscone (B) Università Cattaneo LIUC, Castellanza, VA, Italy e-mail: [email protected] S.A. Osmetti Università Cattolica del Sacro Cuore, Milano, MI, Italy e-mail: [email protected] © Springer International Publishing Switzerland 2017 M.B. Ferraro et al. (eds.), Soft Methods for Data Science, Advances in Intelligent Systems and Computing 456, DOI 10.1007/978-3-319-42972-4_46
373
374
M. Nai Ruscone and S.A. Osmetti
or when their marginal distributions are not in the same family, alternatives to the multivariate normal models must be found. In order to relax the assumption of normality we introduce the use of the copula function to jointly model the dependence structure between the variables and the temporal structure of each process in the model. In particular, we propose a new model for multivariate non normal longitudinal data based on a D-vine copula that is one of a wider class of vine decompositions recently discussed in the context of graphical models (see [2]). We choose the D-vine copula approach because it is an extremely flexible representation of a multivariate distribution that uses bivariate copula (pair-copula) in a hierarchical manner. Smith et al. [6] use D-vine copula to
Data Loading...
