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Box-Cox Transformed Linear Mixed Models for Positive-Valued and Clustered Data

Author

Listed:
  • Shonosuke Sugasawa

    (Graduate School of Economics, The University of Tokyo)

  • Tatsuya Kubokawa

    (Faculty of Economics, The University of Tokyo)

Abstract

The Box-Cox transformation is applied to linear mixed models for analyzing positive and clustered data. The problem is that the maximum likelihood estimator of the transformation parameter is not consistent. To fix it, we suggest a simple and consistent estimator for the transformation parameter based on the moment method. The consistent estimator is used to construct consistent estimators of the parameters involved in the model and to provide an empirical predictor of a linear combination of both fixed and random effects. Second-order accurate prediction intervals for measuring uncertainty of the predictor are derived. Finally, the performance of the proposed procedure is investigated through simulation and empirical studies. --

Suggested Citation

  • Shonosuke Sugasawa & Tatsuya Kubokawa, 2015. "Box-Cox Transformed Linear Mixed Models for Positive-Valued and Clustered Data," CIRJE F-Series CIRJE-F-957, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2015cf957
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2015/2015cf957.pdf
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    References listed on IDEAS

    as
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    3. Jiming Jiang & P. Lahiri, 2006. "Mixed model prediction and small area estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 1-96, June.
    4. Kawakubo, Yuki & Kubokawa, Tatsuya, 2014. "Modified conditional AIC in linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 44-56.
    5. Matthew J. Gurka & Lloyd J. Edwards & Keith E. Muller & Lawrence L. Kupper, 2006. "Extending the Box–Cox transformation to the linear mixed model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(2), pages 273-288, March.
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    Cited by:

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    2. Patricia Dörr & Jan Pablo Burgard, 2019. "Data-driven transformations and survey-weighting for linear mixed models," Research Papers in Economics 2019-16, University of Trier, Department of Economics.

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