Modeling multivariate longitudinal data in the presence of unobserved heterogeneity

A novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity is proposed for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear mixed models with discrete individual random intercepts. This differs from the standard formulation in that 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 it can be affected by some individual socioeconomic characteristics and whether it is possible to identify some homogeneous groups of respondents that share a similar cognitive profile, so that opportune government policy interventions can be addressed. Results identify three homogeneous 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 precise phenomenological characterization.