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Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data

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  • Zhang, Daowen
  • Davidian, Marie

Abstract

Lin and Zhang (J. Roy. Statist. Soc. Ser. B 61 (1999) 381) proposed the generalized additive mixed model (GAMM) as a framework for analysis of correlated data, where normally distributed random effects are used to account for correlation in the data, and proposed to use double penalized quasi-likelihood (DPQL) to estimate the nonparametric functions in the model and marginal likelihood to estimate the smoothing parameters and variance components simultaneously. However, the normal distributional assumption for the random effects may not be realistic in many applications, and it is unclear how violation of this assumption affects ensuing inferences for GAMMs. For a particular class of GAMMs, we propose a conditional estimation procedure built on a conditional likelihood for the response given a sufficient statistic for the random effect, treating the random effect as a nuisance parameter, which thus should be robust to its distribution. In extensive simulation studies, we assess performance of this estimator under a range of conditions and use it as a basis for comparison to DPQL to evaluate the impact of violation of the normality assumption. The procedure is illustrated with application to data from the Multicenter AIDS Cohort Study (MACS).

Suggested Citation

  • Zhang, Daowen & Davidian, Marie, 2004. "Likelihood and conditional likelihood inference for generalized additive mixed models for clustered data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 90-106, October.
    • Handle: RePEc:eee:jmvana:v:91:y:2004:i:1:p:90-106
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    References listed on IDEAS

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    1. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    2. Huageng Tao & Mari Palta & Brian S. Yandell & Michael A. Newton, 1999. "An Estimation Method for the Semiparametric Mixed Effects Model," Biometrics, The International Biometric Society, vol. 55(1), pages 102-110, March.
    3. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    5. Verbeke G. & Spiessens B. & Lesaffre E., 2001. "Conditional Linear Mixed Models," The American Statistician, American Statistical Association, vol. 55, pages 25-34, February.
    6. Daowen Zhang & Marie Davidian, 2001. "Linear Mixed Models with Flexible Distributions of Random Effects for Longitudinal Data," Biometrics, The International Biometric Society, vol. 57(3), pages 795-802, September.
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    2. Francesco Bartolucci & Francesco Valentini & Claudia Pigini, 2023. "Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 529-557, February.

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