Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Abstract

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leão Pinto Jr, Bayesian analysis of a multivariate null intercept error-in-variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763–771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161–178].

Keywords:

• Skew-normal distribution
• Gibbs algorithm
• skewness
• multivariate null intercepts model
• measurement error

Acknowledgements

The authors would like to thank the anonymous referee for helpful comments on this article which improved the paper substantially. The authors acknowledge the partial financial support from Funda\c cão de Amparo à Pesquisa do Estado de São Paulo (FAPESP).