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Hierarchical likelihood methods for nonlinear and generalized linear mixed models with missing data and measurement errors in covariates

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  • Noh, Maengseok
  • Wu, Lang
  • Lee, Youngjo

Abstract

Nonlinear mixed-effects (NLME) models and generalized linear mixed models (GLMM) are popular in the analyses of longitudinal data and clustered data. Covariates are often introduced to partially explain the large between individual (cluster) variation. Many of these covariates, however, contain missing data and/or are measured with errors. In these cases, likelihood inference can be computationally very challenging since the observed data likelihood involves a high-dimensional and intractable integral. Computationally intensive methods such as Monte-Carlo EM algorithms may offer computational difficulties such as very slow convergence or even non-convergence. In this article, we consider hierarchical likelihood methods which approximate the observed-data likelihood using Laplace approximation so completely avoid the intractable integral. We evaluate the methods via simulation and illustrate the methods by two examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:42-51
    DOI: 10.1016/j.jmva.2012.02.011
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    References listed on IDEAS

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    1. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz & Amy H. Herring, 2005. "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 332-346, March.
    2. Joe, Harry, 2008. "Accuracy of Laplace approximation for discrete response mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5066-5074, August.
    3. Germáan Rodríguez & Noreen Goldman, 1995. "An Assessment of Estimation Procedures for Multilevel Models with Binary Responses," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 158(1), pages 73-89, January.
    4. Sung-Cheol Yun & Youngjo Lee & Michael G. Kenward, 2007. "Using Hierarchical Likelihood for Missing Data Problems," Biometrika, Biometrika Trust, vol. 94(4), pages 905-919.
    5. Lang Wu, 2004. "Exact and Approximate Inferences for Nonlinear Mixed-Effects Models With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 700-709, January.
    6. Youngjo Lee & Myoungjin Jang & Woojoo Lee, 2011. "Prediction interval for disease mapping using hierarchical likelihood," Computational Statistics, Springer, vol. 26(1), pages 159-179, March.
    7. 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.
    8. 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.
    9. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    10. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
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    Cited by:

    1. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    2. Yuzhu Tian & Manlai Tang & Maozai Tian, 2018. "Joint modeling for mixed-effects quantile regression of longitudinal data with detection limits and covariates measured with error, with application to AIDS studies," Computational Statistics, Springer, vol. 33(4), pages 1563-1587, December.

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