Statistical Modelling 6 (2006), 231–249
A Bayesian approach to inequality constrained linear mixed models:
estimation and model selection
Bernet S. Kato
Twin Research and Genetic Epidemiology Unit,
St. Thomas' Hospital,
Lambeth Palace Road,
London SE1 7EH
U.K.
eMail:
bernet.kato@kcl.ac.uk
Herbert Hoijtink
Department of Methodology and Statistics,
University of Utrecht,
Utrecht
The Netherlands
Abstract:
Constrained parameter problems arise in a wide variety of
applications. This article deals with estimation and model
selection in linear mixed models with inequality constraints
on the parameters. It is shown that different theories can
be translated into statistical models by putting constraints
on the model parameters yielding a set of competing models.
A new approach based on the principle of encompassing priors
is proposed and used to compute Bayes factors and subsequently
posterior model probabilities. Model selection is based on
posterior model probabilities. The approach is illustrated
using a longitudinal data set.
Keywords:
Bayes factor; encompassing prior; inequality constraints;
linear mixed model; longitudinal data; model selection;
posterior probability; sensitivity analysis
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