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Bayesian inference in measurement error models from objective priors for the bivariate normal distribution

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  • Mário Castro

    (Universidade de São Paulo)

  • Ignacio Vidal

    (Universidad de Talca)

Abstract

In regression analysis, when the covariates are not exactly observed, measurement error models extend the usual regression models toward a more realistic representation of the covariates. It is common in the literature to directly propose prior distributions for the parameters in normal measurement error models. Posterior inference requires Markov chain Monte Carlo (MCMC) computations. However, the regression model can be seen as a reparameterization of the bivariate normal distribution. In this paper, general results for objective Bayesian inference under the bivariate normal distribution were adapted to the regression framework. So, posterior inferences for the structural parameters of a measurement error model under a great variety of priors were obtained in a simple way. The methodology is illustrated by using five common prior distributions showing good performance for all prior distributions considered. MCMC methods are not necessary at all. Model assessment is also discussed. Results from a simulation study and applications to real data sets are reported.

Suggested Citation

  • Mário Castro & Ignacio Vidal, 2019. "Bayesian inference in measurement error models from objective priors for the bivariate normal distribution," Statistical Papers, Springer, vol. 60(4), pages 1059-1078, August.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-016-0863-7
    DOI: 10.1007/s00362-016-0863-7
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    References listed on IDEAS

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    1. Heleno Bolfarine & Lisbeth Cordani, 1993. "Estimation of a structural linear regression model with a known reliability ratio," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 531-540, September.
    2. Mário Castro & Heleno Bolfarine & M. Galea, 2013. "Bayesian inference in measurement error models for replicated data," Environmetrics, John Wiley & Sons, Ltd., vol. 24(1), pages 22-30, February.
    3. Vidal, Ignacio & Iglesias, Pilar, 2008. "Comparison between a measurement error model and a linear model without measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 92-102, September.
    4. Victor Lachos & Vicente Cancho & Reiko Aoki, 2010. "Bayesian analysis of skew-t multivariate null intercept measurement error model," Statistical Papers, Springer, vol. 51(3), pages 531-545, September.
    5. Fang, Kai-Tai & Li, Runze, 1999. "Bayesian Statistical Inference on Elliptical Matrix Distributions," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 66-85, July.
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