IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v106y2012icp1-16.html
   My bibliography  Save this article

Parametric bootstrap methods for bias correction in linear mixed models

Author

Listed:
  • Kubokawa, Tatsuya
  • Nagashima, Bui

Abstract

The empirical best linear unbiased predictor (EBLUP) in the linear mixed model (LMM) is useful for the small area estimation, and the estimation of the mean squared error (MSE) of EBLUP is important as a measure of uncertainty of EBLUP. To obtain a second-order unbiased estimator of the MSE, the second-order bias correction has been derived based on Taylor series expansions. However, this approach is hard to implement in complicated models with many unknown parameters like variance components, since we need to compute asymptotic bias, variance and covariance for estimators of unknown parameters as well as partial derivatives of some quantities. A similar difficulty occurs in the construction of confidence intervals based on EBLUP with second-order correction and in the derivation of second-order bias correction in the Akaike Information Criterion (AIC) and the conditional AIC. To avoid such difficulty in the derivation of second-order bias correction in these problems, the parametric bootstrap methods are suggested in this paper, and their second-order justifications are established. Finally, performances of the suggested procedures are numerically investigated in comparison with some existing procedures given in the literature.

Suggested Citation

  • Kubokawa, Tatsuya & Nagashima, Bui, 2012. "Parametric bootstrap methods for bias correction in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 1-16.
    • Handle: RePEc:eee:jmvana:v:106:y:2012:i:c:p:1-16
    DOI: 10.1016/j.jmva.2011.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11002168
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2011.12.002?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. Gauri Sankar Datta & J. N. K. Rao & David Daniel Smith, 2005. "On measuring the variability of small area estimators under a basic area level model," Biometrika, Biometrika Trust, vol. 92(1), pages 183-196, March.
    2. Gauri Sankar Datta & Malay Ghosh & David Daniel Smith & Parthasarathi Lahiri, 2002. "On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 139-152, March.
    3. Gauri Datta & Tatsuya Kubokawa & Isabel Molina & J. Rao, 2011. "Estimation of mean squared error of model-based small area estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 367-388, August.
    4. Hua Liang & Hulin Wu & Guohua Zou, 2008. "A note on conditional aic for linear mixed-effects models," Biometrika, Biometrika Trust, vol. 95(3), pages 773-778.
    5. Peter Hall & Tapabrata Maiti, 2006. "On parametric bootstrap methods for small area prediction," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 221-238, April.
    6. Tatsuya Kubokawa, 2010. "On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy," CIRJE F-Series CIRJE-F-754, CIRJE, Faculty of Economics, University of Tokyo.
    7. Doornik, Jurgen A. & Ooms, Marius, 2003. "Computational aspects of maximum likelihood estimation of autoregressive fractionally integrated moving average models," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 333-348, March.
    8. Basu, Ruma & Ghosh, J. K. & Mukerjee, Rahul, 2003. "Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 197-203, June.
    9. Florin Vaida & Suzette Blanchard, 2005. "Conditional Akaike information for mixed-effects models," Biometrika, Biometrika Trust, vol. 92(2), pages 351-370, June.
    10. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yuki Kawakubo & Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Conditional AIC under Covariate Shift with Application to Small Area Prediction," CIRJE F-Series CIRJE-F-944, CIRJE, Faculty of Economics, University of Tokyo.
    2. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    3. Tatsuya Kubokawa, 2012. "Mixed Effects Prediction under Benchmarking and Applications to Small Area Estimation," CIRJE F-Series CIRJE-F-832, CIRJE, Faculty of Economics, University of Tokyo.
    4. Flores-Agreda, Daniel & Cantoni, Eva, 2019. "Bootstrap estimation of uncertainty in prediction for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 1-17.
    5. Yuki Kawakubo & Tatsuya Kubokawa, 2013. "Modfiied Conditional AIC in Linear Mixed Models," CIRJE F-Series CIRJE-F-895, CIRJE, Faculty of Economics, University of Tokyo.

    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. Tatsuya Kubokawa, 2009. "A Review of Linear Mixed Models and Small Area Estimation," CIRJE F-Series CIRJE-F-702, CIRJE, Faculty of Economics, University of Tokyo.
    2. Tatsuya Kubokawa & Bui Nagashima, 2011. "Parametric Bootstrap Methods for Bias Correction in Linear Mixed Models," CIRJE F-Series CIRJE-F-801, CIRJE, Faculty of Economics, University of Tokyo.
    3. Tatsuya Kubokawa, 2010. "On Measuring Uncertainty of Small Area Estimators with Higher Order Accuracy," CIRJE F-Series CIRJE-F-754, CIRJE, Faculty of Economics, University of Tokyo.
    4. Tatsuya Kubokawa, 2009. "Corrected Empirical Bayes Confidence Intervals in Nested Error Regression Models," CIRJE F-Series CIRJE-F-632, CIRJE, Faculty of Economics, University of Tokyo.
    5. Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "Estimation and Prediction Intervals in Transformed Linear Mixed Models," CIRJE F-Series CIRJE-F-929, CIRJE, Faculty of Economics, University of Tokyo.
    6. Simona Buscemi & Antonella Plaia, 2020. "Model selection in linear mixed-effect models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 529-575, December.
    7. Masahiro Kojima & Tatsuya Kubokawa, 2013. "Bartlett Adjustments for Hypothesis Testing in Linear Models with General Error Covariance Matrices," CIRJE F-Series CIRJE-F-884, CIRJE, Faculty of Economics, University of Tokyo.
    8. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    9. Katarzyna Reluga & María‐José Lombardía & Stefan Sperlich, 2023. "Simultaneous inference for linear mixed model parameters with an application to small area estimation," International Statistical Review, International Statistical Institute, vol. 91(2), pages 193-217, August.
    10. Overholser, Rosanna & Xu, Ronghui, 2014. "Effective degrees of freedom and its application to conditional AIC for linear mixed-effects models with correlated error structures," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 160-170.
    11. Hirose, Masayo Yoshimori, 2017. "Non-area-specific adjustment factor for second-order efficient empirical Bayes confidence interval," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 67-78.
    12. Kubokawa, Tatsuya, 2011. "Conditional and unconditional methods for selecting variables in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 641-660, March.
    13. Sugasawa, Shonosuke & Kubokawa, Tatsuya, 2016. "On conditional prediction errors in mixed models with application to small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 18-33.
    14. Shonosuke Sugasawa & Tatsuya Kubokawa, 2014. "On Conditional Mean Squared Errors of Empirical Bayes Estimators in Mixed Models with Application to Small Area Estimation," CIRJE F-Series CIRJE-F-934, CIRJE, Faculty of Economics, University of Tokyo.
    15. Sugasawa, Shonosuke & Kawakubo, Yuki & Datta, Gauri Sankar, 2019. "Observed best selective prediction in small area estimation," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 383-392.
    16. Yu, Dalei & Zhang, Xinyu & Yau, Kelvin K.W., 2013. "Information based model selection criteria for generalized linear mixed models with unknown variance component parameters," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 245-262.
    17. J. N. K. Rao, 2015. "Inferential issues in model-based small area estimation: some new developments," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 16(4), pages 491-510, December.
    18. repec:csb:stintr:v:17:y:2016:i:1:p:9-24 is not listed on IDEAS
    19. Erciulescu Andreea L. & Fuller Wayne A., 2016. "Small Area Prediction Under Alternative Model Specifications," Statistics in Transition New Series, Statistics Poland, vol. 17(1), pages 9-24, March.
    20. Lixia Diao & David D. Smith & Gauri Sankar Datta & Tapabrata Maiti & Jean D. Opsomer, 2014. "Accurate Confidence Interval Estimation of Small Area Parameters Under the Fay–Herriot Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 497-515, June.
    21. Cantoni, Eva & Jacot, Nadège & Ghisletta, Paolo, 2024. "Review and comparison of measures of explained variation and model selection in linear mixed-effects models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 150-168.

    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:106:y:2012:i:c:p:1-16. 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.