Robust estimation of the correlation matrix of longitudinal data

We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ = DLL ⊤ D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D , and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t -distributions with unknown degrees of freedom. We develop a Fisher scoring algorithm for computing the maximum likelihood estimator of the parameters when the nonredundant and unconstrained entries of ( L , D ) are modeled parsimoniously using covariates. We compare our results with those based on the modified Cholesky decomposition of the form LD 2 L ⊤ using simulations and a real dataset.