Marta Nai Ruscone

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 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.

Scale Reliability Evaluation for a-priori Clustered Data

According to the classical measurement theory, the reliability of a set of indicators related to a latent variable describing a true measure can be assessed through the Cronbach’s \(\alpha\) index. The Cronbach’s α index can be used for τ-equivalent measures and for parallel measures and represents a lower bound for the reliability value in presence of congeneric measures, for which the assessment can properly be made only ex post, once the loading coefficients have been estimated, e.g. by means of a structural equation model with latent variables.Once assumed the existence of an a-priori segmentation based upon a categorical variable Z, we test whether the construct is reliable all over the groups. In this case the measurement model is the same across groups, which means that loadings are equal within each group as well as they do not vary across groups. A formulation of the Cronbach’s α coefficient is considered according to the decomposition of pairwise covariances in a clustered framework, and a test procedure assessing the possible presence of congeneric measures in a multigroup framework is proposed.