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Efficient parametrisations for normal linear mixed models

Efficient parametrisations for normal linear mixed models
Efficient parametrisations for normal linear mixed models
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.
gibbs sampler, hierarchical model, identifiability, laird-ware model, markov chain monte carlo, nested models, random effects model, rate of convergence
0006-3444
479-488
Gelfand, Alan E.
1dc59cf1-5e5f-4001-b1f9-92b0a8e2f64f
Sahu, Sujit K.
33f1386d-6d73-4b60-a796-d626721f72bf
Carlin, Bradley P.
87e22ce0-eaee-49bc-ac19-2c41da442620
Gelfand, Alan E.
1dc59cf1-5e5f-4001-b1f9-92b0a8e2f64f
Sahu, Sujit K.
33f1386d-6d73-4b60-a796-d626721f72bf
Carlin, Bradley P.
87e22ce0-eaee-49bc-ac19-2c41da442620

Gelfand, Alan E., Sahu, Sujit K. and Carlin, Bradley P. (1995) Efficient parametrisations for normal linear mixed models. Biometrika, 82 (3), 479-488. (doi:10.1093/biomet/82.3.479).

Record type: Article

Abstract

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.

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More information

Published date: 1995
Keywords: gibbs sampler, hierarchical model, identifiability, laird-ware model, markov chain monte carlo, nested models, random effects model, rate of convergence
Organisations: Statistics

Identifiers

Local EPrints ID: 30014
URI: https://eprints.soton.ac.uk/id/eprint/30014
ISSN: 0006-3444
PURE UUID: 1b3573e6-de93-430f-a8ad-af2551ce5beb
ORCID for Sujit K. Sahu: ORCID iD orcid.org/0000-0003-2315-3598

Catalogue record

Date deposited: 11 May 2007
Last modified: 06 Jun 2018 12:52

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