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A Bayesian approach to inequality constrained linear mixed models: estimation and model selection

Twin Research and Genetic Epidemiology Unit, St Thomas' Hospital, London, UK, bernet.kato{at}kcl.ac.uk

Herbert Hoijtink

Department of Methodology and Statistics, University of Utrecht, Utrecht, The Netherlands

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.

Key Words: Bayes factor • encompassing prior • inequality constraints • linear mixed model • longitudinal data • model selection • posterior probability • sensitivity analysis

Statistical Modelling, Vol. 6, No. 3, 231-249 (2006)
DOI: 10.1191/1471082X06st119oa


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