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A hybrid estimator in nonlinear and generalised linear mixed effects models

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  • Tze Leung Lai

Abstract

A hybrid method that combines Laplace's approximation and Monte Carlo simulations to evaluate integrals in the likelihood function is proposed for estimation of the parameters in nonlinear mixed effects models that assume a normal parametric family for the random effects. Simulations show that these parametric estimates of fixed effects are close to the nonparametric estimates even though the mixing distribution is far from the assumed normal parametric family. An asymptotic theory of this hybrid method for parametric estimation without requiring the true mixing distribution to belong to the assumed parametric family is developed to explain these results. This hybrid method and its asymptotic theory are also extended to generalised linear mixed effects models. Copyright Biometrika Trust 2003, Oxford University Press.

Suggested Citation

  • 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.
  • Handle: RePEc:oup:biomet:v:90:y:2003:i:4:p:859-879
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    Cited by:

    1. Tze Leung Lai & Mei-Chiung Shih & Samuel Po-Shing Wong, 2006. "Flexible Modeling via a Hybrid Estimation Scheme in Generalized Mixed Models for Longitudinal Data," Biometrics, The International Biometric Society, vol. 62(1), pages 159-167, March.
    2. 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.
    3. Kauermann, Goran & Xu, Ronghui & Vaida, Florin, 2008. "Stacked Laplace-EM algorithm for duration models with time-varying and random effects," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2514-2528, January.

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