  This paper focuses on the multivariate linear mixed-effects model, including
all the correlations between the random effects when the marginal residual
terms are assumed uncorrelated and homoscedastic with possibly different
standard deviations. The random effects covariance matrix is Cholesky
factorized to directly estimate the variance components of these random
effects. This strategy enables a consistent estimate of the random effects
covariance matrix which, generally, has a poor estimate when it is grossly (or
directly) estimated, using the estimating methods such as the EM algorithm. By
using simulated data sets, we compare the estimates based on the present method
with the EM algorithm-based estimates. We provide an illustration by using the
real-life data concerning the study of the child's immune against malaria in
Benin (West Africa).
