Efficient Parametrisations for Normal Linear Mixed Models
针对正态线性混合模型，提出简单分层中心化重参数化方法，通过分析论证和模拟研究证明其能有效改善参数估计的收敛效率，对纵向数据等应用场景尤其有用。
The generality and easy programmability of modern sampling-based methods for maximisation of likelihoods and summarisation of posterior distributions have led to a tremendous increase in the complexity and dimensionality of the statistical models used in practice. However, these methods can often be extremely slow to converge, due to high correlations between, or weak identifiability of, certain model parameters. We present simple hierarchical centring reparametrisations that often give improved convergence for a broad class of normal linear mixed models. In particular, we study the two-stage hierarchical normal linear model, the Laird-Ware model for longitudinal data, and a general structure for hierarchically nested linear models. Using analytical arguments, simulation studies, and an example involving clinical markers of acquired immune deficiency syndrome (aids), we indicate when reparametrisation is likely to provide substantial gains in efficiency.