Bayesian measurement error models using finite mixtures of scale mixtures of skew-normal distributions

Abstract

We present a proposal to deal with the non-normality issue in the context of regression models with measurement errors when both the response and the explanatory variable are observed with error. We extend the normal model by jointly modelling the unobserved covariate and the random errors by a finite mixture of scale mixture of skew-normal distributions. This approach allows us to model data with great flexibility, accommodating skewness, heavy tails, and multi-modality. The main virtue of considering measurement error models under the class of scale mixtures of skew-normal distributions is that they have a nice hierarchical representation which allows easy implementation of inference. In order to illustrate the usefulness of the proposed method some simulation studies are presented  and a real dataset (Systemic lupus erythematosus) is analyzed.

Keywords:

• Bayesian estimation
• finite mixtures
• MCMC
• skew normal distribution
• scale mixtures of skew normal

Acknowledgments

The authors would like to thank an anonymous referee for insightful comments which substantially improved the paper. The research was supported by Universidade Federal do Amazonas (UFAM), Coordenação de Aperfeioamento de Pessoal de Nível Superior (CAPES) and CNPq grants from the Brazilian federal government, and by FAPEAM grants from the government of the State of Amazonas, Brazil.

Disclosure statement

No potential conflict of interest was reported by the authors.