EFFICIENT PARAMETRIZATIONS FOR NORMAL LINEAR MIXED MODELS

The generality and easy programmability of modern sampling-based metho ds for maximisation of likelihoods and summarisation of posterior dist ributions have led to a tremendous increase in the complexity and dime nsionality of the statistical models used in practice. However, these methods can often be extremely slow to converge, due to high correlati ons between, or weak identifiability of, certain model parameters. We present simple hierarchical centring reparametrisations that often giv e improved convergence for a broad class of normal linear mixed models . In particular, we study the two-stage hierarchical normal linear mod el, the Laird-Ware model for longitudinal data, and a general structur e for hierarchically nested linear models. Using analytical arguments, simulation studies, and an example involving clinical markers of acqu ired immune deficiency syndrome (AIDS), We indicate when reparametrisa tion is likely to provide substantial gains in efficiency.