Covariance pattern mixture models for multivariate longitudinal data with application to the Health and Retirement Study
Laura Anderlucci, Cinzia Viroli · arXiv (Cornell University) · 2014
We propose a novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear mixed model with discrete individual random intercepts, but differently from the standard formulation, the proposed Covariance Pattern Mixture Model (CPMM) does not require the usual local independence assumption; therefore, it is able to simultaneously model the heterogeneity, the association among the responses and the temporal dependence structure. We focus on the investigation of temporal patterns related to the cognitive functioning in retired American respondents, aiming to understand whether its behaviour can be affected by some individual socio-economical characteristics and whether it is possible to identify some homogenous groups of respondents that share a similar cognitive profile, so that opportune policy interventions can be addressed. Results identify three homogenous clusters of individuals with specific cognitive functioning, consistent with the class conditional distribution of the covariates. The flexibility of CPMM allows for a different contribution of each regressor on the responses according to group membership. In so doing, the identified groups receive a global and punctual phenomenal characterization.