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Hierarchical-likelihood approach for nonlinear mixed-effects models

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  • Noh, Maengseok
  • Lee, Youngjo

Abstract

The restricted maximum likelihood (REML) procedure is useful for inferences about variance components in linear mixed models (LMMs). However, its extension to nonlinear mixed models (NLMMs) is often hampered by analytically intractable integrals. For NLMMs various estimation methods have been suggested, but they have suffered from unsatisfactory biases. In this paper we propose a statistically and computationally efficient REML procedure, based upon hierarchical likelihood. Numerical studies show that the proposed method reduces the biases in the existing methods that we studied. We also study how the current REML procedure for LMMs can be modified to compute the proposed estimators.

Suggested Citation

  • Noh, Maengseok & Lee, Youngjo, 2008. "Hierarchical-likelihood approach for nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3517-3527, March.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3517-3527
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    References listed on IDEAS

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    1. Wolfinger, Russell D. & Xihong Lin, 1997. "Two Taylor-series approximation methods for nonlinear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 25(4), pages 465-490, September.
    2. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    3. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
    4. Tze Leung Lai, 2003. "Nonparametric estimation in nonlinear mixed effects models," Biometrika, Biometrika Trust, vol. 90(1), pages 1-13, March.
    5. Tze Leung Lai, 2003. "A hybrid estimator in nonlinear and generalised linear mixed effects models," Biometrika, Biometrika Trust, vol. 90(4), pages 859-879, December.
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    1. Noh, Maengseok & Wu, Lang & Lee, Youngjo, 2012. "Hierarchical likelihood methods for nonlinear and generalized linear mixed models with missing data and measurement errors in covariates," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 42-51.
    2. Yu, Dalei & Yau, Kelvin K.W., 2012. "Conditional Akaike information criterion for generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 629-644.
    3. Commenges, D. & Jolly, D. & Drylewicz, J. & Putter, H. & Thiébaut, R., 2011. "Inference in HIV dynamics models via hierarchical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 446-456, January.

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