Robust estimation for the correlation matrix of multivariate longitudinal data

Abstract

Modelling the covariance structure of multivariate longitudinal data is more challenging than its univariate counterpart, owing to the complex correlated structure among multiple responses. Furthermore, there are little methods focusing on the robustness of estimating the corresponding correlation matrix. In this paper, we propose an alternative Cholesky block decomposition (ACBD) for the covariance matrix of multivariate longitudinal data. The new unconstrained parameterization is capable to automatically eliminate the positive definiteness constraint of the covariance matrix and robustly estimate the correlation matrix with respect to the model misspecifications of the nested prediction error covariance matrices. The entries of the new decomposition are modelled by regression models, and the maximum likelihood estimators of the regression parameters in joint mean–covariance models are computed by a quasi-Fisher iterative algorithm. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and real data analysis illustrate that the new method performs well.