Bayesian inference in a heteroscedastic replicated measurement error model using heavy-tailed distributions

ABSTRACT

We introduce a multivariate heteroscedastic measurement error model for replications under scale mixtures of normal distribution. The model can provide a robust analysis and can be viewed as a generalization of multiple linear regression from both model structure and distribution assumption. An efficient method based on Markov Chain Monte Carlo is developed for parameter estimation. The deviance information criterion and the conditional predictive ordinates are used as model selection criteria. Simulation studies show robust inference behaviours of the model against both misspecification of distributions and outliers. We work out an illustrative example with a real data set on measurements of plant root decomposition.

KEYWORDS:

• Heteroscedasticity
• Markov Chain Monte Carlo
• multiple regression
• scale mixtures of normal
• robustness

Acknowledgements

We are grateful to Dr. S. Smart, the associate editor and the referees for their helpful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China [grant no. 11301278] and the MOE (Ministry of Education in China) Project of Humanities and Social Sciences [grant no. 13YJC910001].