Efficient parametrisations for normal linear mixed models

Alan E. Gelfand, Sujit K. Sahu, Bradley P. Carlin

Research output: Contribution to journalArticlepeer-review

232 Scopus citations

Abstract

SUMMARY: 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.

Original languageEnglish (US)
Pages (from-to)479-488
Number of pages10
JournalBiometrika
Volume82
Issue number3
DOIs
StatePublished - Sep 1995

Keywords

  • Gibbs sampler
  • Hierarchical model
  • Identifiability
  • Laird-Ware model
  • Markov chain Monte Carlo
  • Nested models
  • Random effects model
  • Rate of convergence

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