IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v153y2017icp52-63.html
   My bibliography  Save this article

Bayesian estimators in uncertain nested error regression models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1630094X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.09.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tamal Ghosh & Malay Ghosh & Jerry J. Maples & Xueying Tang, 2022. "Multivariate Global-Local Priors for Small Area Estimation," Stats, MDPI, vol. 5(3), pages 1-16, July.
    2. Datta, Gauri S. & Torabi, Mahmoud & Rao, J.N.K. & Liu, Benmei, 2018. "Small area estimation with multiple covariates measured with errors: A nested error linear regression approach of combining multiple surveys," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 49-59.
    3. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2017. "Transforming response values in small area prediction," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 47-60.
    4. Harm Jan Boonstra & Jan van den Brakel & Sumonkanti Das, 2021. "Multilevel time series modelling of mobility trends in the Netherlands for small domains," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 184(3), pages 985-1007, July.
    5. Serena Arima & William R. Bell & Gauri S. Datta & Carolina Franco & Brunero Liseo, 2017. "Multivariate Fay–Herriot Bayesian estimation of small area means under functional measurement error," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1191-1209, October.
    6. Chakraborty Adrijo & Datta Gauri Sankar & Mandal Abhyuday, 2016. "A Two-Component Normal Mixture Alternative to the Fay-Herriot Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 67-90, March.
    7. Sun, Hanmei & Jiang, Jiming & Nguyen, Thuan & Luan, Yihui, 2018. "Best look-alike prediction: Another look at the Bayesian classifier and beyond," Statistics & Probability Letters, Elsevier, vol. 143(C), pages 37-42.
    8. Priyanka Anjoy, 2023. "Hierarchical Bayes Measurement Error Small Area Model for Estimation of Disaggregated Level Workers Mobility Pattern in India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 21(2), pages 339-361, June.
    9. repec:csb:stintr:v:17:y:2016:i:1:p:67-90 is not listed on IDEAS
    10. Malay Ghosh, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    11. Shonosuke Sugasawa & Tatsuya Kubokawa & Kota Ogasawara, 2017. "Empirical Uncertain Bayes Methods in Area-level Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(3), pages 684-706, September.
    12. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2020. "A Fay–Herriot model when auxiliary variables are measured with error," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 166-195, March.
    13. 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.
    14. Shonosuke Sugasawa & Hiromasa Tamae & Tatsuya Kubokawa, 2017. "Bayesian Estimators for Small Area Models Shrinking Both Means and Variances," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 150-167, March.
    15. Adrijo Chakraborty & Gauri Sankar Datta & Abhyuday Mandal, 2016. "A Two-Component Normal Mixture Alternative To The Fay-Herriot Model," Statistics in Transition New Series, Polish Statistical Association, vol. 17(1), pages 67-90, March.
    16. Ghosh Malay, 2020. "Small area estimation: its evolution in five decades," Statistics in Transition New Series, Polish Statistical Association, vol. 21(4), pages 1-22, August.
    17. Domingo Morales & Joscha Krause & Jan Pablo Burgard, 2022. "On the Use of Aggregate Survey Data for Estimating Regional Major Depressive Disorder Prevalence," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 344-368, March.
    18. Jan Pablo Burgard & María Dolores Esteban & Domingo Morales & Agustín Pérez, 2021. "Small area estimation under a measurement error bivariate Fay–Herriot model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 79-108, March.
    19. Elaheh Torkashvand & Mohammad Jafari Jozani & Mahmoud Torabi, 2017. "Clustering in small area estimation with area level linear mixed models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(4), pages 1253-1279, October.
    20. Buddhavarapu, Prasad & Bansal, Prateek & Prozzi, Jorge A., 2021. "A new spatial count data model with time-varying parameters," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 566-586.
    21. Mumtaz, Haroon & Theodoridis, Konstantinos, 2017. "Common and country specific economic uncertainty," Journal of International Economics, Elsevier, vol. 105(C), pages 205-216.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:52-63. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.