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Effect of Smoothing in Generalized Linear Mixed Models on the Estimation of Covariance Parameters for Longitudinal Data

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  • Mullah Muhammad Abu Shadeque

    (Department of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Canada)

  • Benedetti Andrea

    (Departments of Medicine and of Epidemiology, Biostatistics and Occupational Health, McGill University, Montreal, Canada)

Abstract

Besides being mainly used for analyzing clustered or longitudinal data, generalized linear mixed models can also be used for smoothing via restricting changes in the fit at the knots in regression splines. The resulting models are usually called semiparametric mixed models (SPMMs). We investigate the effect of smoothing using SPMMs on the correlation and variance parameter estimates for serially correlated longitudinal normal, Poisson and binary data. Through simulations, we compare the performance of SPMMs to other simpler methods for estimating the nonlinear association such as fractional polynomials, and using a parametric nonlinear function. Simulation results suggest that, in general, the SPMMs recover the true curves very well and yield reasonable estimates of the correlation and variance parameters. However, for binary outcomes, SPMMs produce biased estimates of the variance parameters for high serially correlated data. We apply these methods to a dataset investigating the association between CD4 cell count and time since seroconversion for HIV infected men enrolled in the Multicenter AIDS Cohort Study.

Suggested Citation

  • Mullah Muhammad Abu Shadeque & Benedetti Andrea, 2016. "Effect of Smoothing in Generalized Linear Mixed Models on the Estimation of Covariance Parameters for Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 12(2), pages 1-19, November.
    • Handle: RePEc:bpj:ijbist:v:12:y:2016:i:2:p:19:n:3
    DOI: 10.1515/ijb-2015-0026
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    References listed on IDEAS

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    1. 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.
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