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Generalized prediction intervals for BLUPs in mixed models

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  • Gamage, Jinadasa
  • Mathew, Thomas
  • Weerahandi, Samaradasa

Abstract

A prediction interval is derived for the BLUP (Best Linear Unbiased Predictor) in mixed models involving a single random effect of interest, using the generalized inference approach. The resulting prediction interval is referred to as a generalized prediction interval. The solution in the case of the simplest balanced random effects model is first derived to provide better insight into the approach. Extensions to the unbalanced case as well as to a general model are then provided. A simulation study is carried out to show the advantage of the proposed interval compared to the ML and REML based intervals available from widely used software packages such as SAS and R/S+. The estimated coverage probabilities show that the generalized prediction interval exhibits substantially better performance compared to ML and REML based intervals; the latter intervals were found to be highly conservative.

Suggested Citation

  • Gamage, Jinadasa & Mathew, Thomas & Weerahandi, Samaradasa, 2013. "Generalized prediction intervals for BLUPs in mixed models," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 226-233.
    • Handle: RePEc:eee:jmvana:v:120:y:2013:i:c:p:226-233
    DOI: 10.1016/j.jmva.2013.05.011
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    References listed on IDEAS

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    1. Frees,Edward W., 2004. "Longitudinal and Panel Data," Cambridge Books, Cambridge University Press, number 9780521828284.
    2. Frees,Edward W., 2004. "Longitudinal and Panel Data," Cambridge Books, Cambridge University Press, number 9780521535380.
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    1. Samaradasa Weerahandi & Ching-Ray Yu, 2020. "Exact distributions of statistics for making inferences on mixed models under the default covariance structure," Journal of Statistical Distributions and Applications, Springer, vol. 7(1), pages 1-14, December.
    2. Sam W & Peijin X & Ching RY & Kelly HZ, 2018. "Improved EBLUPs in Mixed-Effects Regression Models," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(4), pages 78-86, January.
    3. Mathew, Thomas & Menon, Sandeep & Perevozskaya, Inna & Weerahandi, Samaradasa, 2016. "Improved prediction intervals in heteroscedastic mixed-effects models," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 48-53.

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