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Bayesian estimators in uncertain nested error regression models

Author

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  • Sugasawa, Shonosuke
  • Kubokawa, Tatsuya

Abstract

Nested error regression models are useful tools for the analysis of grouped data, especially in the context of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in each area is expressed as a mixture of a normal distribution and a positive mass at 0. For the estimation of the model parameters and prediction of the random effects, an objective Bayesian inference is proposed by setting non-informative prior distributions on the model parameters. Under mild sufficient conditions, it is shown that the posterior distribution is proper and the posterior variances are finite, confirming the validity of posterior inference. To generate samples from the posterior distribution, a Gibbs sampling method is provided with familiar forms for all the full conditional distributions. This paper also addresses the problem of predicting finite population means, and a sampling-based method is suggested to tackle this issue. Finally, the proposed model is compared with the conventional nested error regression model through simulation and empirical studies.

Suggested Citation

  • Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Bayesian estimators in uncertain nested error regression models," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 52-63.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:52-63
    DOI: 10.1016/j.jmva.2016.09.011
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    References listed on IDEAS

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    1. Torabi, Mahmoud, 2012. "Small area estimation using survey weights under a nested error linear regression model with structural measurement error," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 52-60.
    2. Datta, Gauri S. & Hall, Peter & Mandal, Abhyuday, 2011. "Model Selection by Testing for the Presence of Small-Area Effects, and Application to Area-Level Data," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 362-374.
    3. Malay Ghosh & Karabi Sinha & Dalho Kim, 2006. "Empirical and Hierarchical Bayesian Estimation in Finite Population Sampling under Structural Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 591-608, September.
    4. 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.
    5. Shonosuke Sugasawa & Tatsuya Kubokawa, 2015. "Heteroscedastic Nested Error Regression Models with Variance Functions," CIRJE F-Series CIRJE-F-978, CIRJE, Faculty of Economics, University of Tokyo.
    6. Serena Arima & Gauri S. Datta & Brunero Liseo, 2015. "Bayesian Estimators for Small Area Models when Auxiliary Information is Measured with Error," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 518-529, June.
    7. Gauri Sankar Datta & Abhyuday Mandal, 2015. "Small Area Estimation With Uncertain Random Effects," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1735-1744, December.
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