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A robust Bayesian approach to null intercept measurement error model with application to dental data

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  • Ghosh, Pulak
  • Bayes, C.L.
  • Lachos, V.H.

Abstract

Measurement error models often arise in epidemiological and clinical research. Usually, in this set up it is assumed that the latent variable has a normal distribution. However, the normality assumption may not be always correct. Skew-normal/independent distribution is a class of asymmetric thick-tailed distributions which includes the skew-normal distribution as a special case. In this paper, we explore the use of skew-normal/independent distribution as a robust alternative to null intercept measurement error model under a Bayesian paradigm. We assume that the random errors and the unobserved value of the covariate (latent variable) follows jointly a skew-normal/independent distribution, providing an appealing robust alternative to the routine use of symmetric normal distribution in this type of model. Specific distributions examined include univariate and multivariate versions of the skew-normal distribution, the skew-t distributions, the skew-slash distributions and the skew contaminated normal distributions. The methods developed is illustrated using a real data set from a dental clinical trial.

Suggested Citation

  • Ghosh, Pulak & Bayes, C.L. & Lachos, V.H., 2009. "A robust Bayesian approach to null intercept measurement error model with application to dental data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1066-1079, February.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:4:p:1066-1079
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    References listed on IDEAS

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    1. Reiko Aoki & Hereno Bolfarine & Julio Singer, 2001. "Null intercept measurement error regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 441-457, December.
    2. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
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    4. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    5. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    6. Reiko Aoki & Jorge Achcar & Heleno Bolfarine & Julio Singer, 2003. "Bayesian analysis of null intercept errors-in-variables regression for pretest/post-test data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 30(1), pages 3-12.
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