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An improved approximation to the precision of fixed effects from restricted maximum likelihood

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  • Kenward, Michael G.
  • Roger, James H.

Abstract

An approximate small sample variance estimator for fixed effects from the multivariate normal linear model, together with appropriate inference tools based on a scaled F pivot, is now well established in practice and there is a growing literature on its properties in a variety of settings. Although effective under linear covariance structures, there are examples of nonlinear structures for which it does not perform as well. The cause of this problem is shown to be a missing term in the underlying Taylor series expansion which accommodates the bias in the estimators of the parameters of the covariance structure. The form of this missing term is derived, and then used to adjust the small sample variance estimator. The behaviour of the resulting estimator is explored in terms of invariance under transformation of the covariance parameters and also using a simulation study. It is seen to perform successfully in the way predicted from its derivation.

Suggested Citation

  • Kenward, Michael G. & Roger, James H., 2009. "An improved approximation to the precision of fixed effects from restricted maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2583-2595, May.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:7:p:2583-2595
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    References listed on IDEAS

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    1. Michael G. Kenward, 1987. "A Method for Comparing Profiles of Repeated Measurements," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 296-308, November.
    2. Yutaka Yasui & Ziding Feng & Paula Diehr & Dale McLerran & Shirley A. A. Beresford & Charles E. McCulloch, 2004. "Evaluation of Community-Intervention Trials via Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 60(4), pages 1043-1052, December.
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