ABSTRACT
The Cholesky decomposition is a method for decomposing a matrix into the product of a lower triangular matrix and its transpose. Pan and MacKenzie use the modified Cholesky decomposition for joint modelling of the mean and covariance in longitudinal studies. Pourahmadi develop an approach for simultaneously modelling several covariance matrices via this decomposition, thereby giving an alternative to common principal components analysis for longitudinal data. McNicholas and Murphy a use a Gaussian mixture model with a modified Cholesky-decomposed covariance structure for each component to model longitudinal data. Each member of the Cholesky-decomposed Gaussian mixture model family has a natural interpretation for longitudinal data. Simulated data are used to illustrate the model-based clustering of longitudinal data. Parameter estimation for most of the other models is similar to that for the VEA model, with the two exceptions being the EVA and EVI models.
