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Fully Modified GEE Modeling of Correlated Univariate Outcomes

In: Modeling Correlated Outcomes Using Extensions of Generalized Estimating Equations and Linear Mixed Modeling

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  • George J. Knafl

    (University of North Carolina at Chapel Hill, School of Nursing)

Abstract

GEE modeling can be fully modified to account for the dependence of the likelihood on mean parameters as well as on dispersion parameters rather than using the standard GEE estimating equations for the mean parameters. General formulas are presented for gradient vectors and Hessian matrices as well as detailed formulas under alternate regression types and link functions, covering commonly used distributions including the normal, Poisson, Bernoulli, exponential, and inverse Gaussian distributions. Adjustments to the estimation process are provided to account for maximizing the likelihood rather than minimizing the absolute value of the gradient. The special case of singleton univariate outcomes, that is, independent measurements, is addressed. It can be used to generate initial estimates for parameter estimation. Standard generalized linear modeling can be used to generate initial estimates of mean parameters for standard GEE modeling. Handling of initial estimates of both mean and dispersion parameters as needed for partially modified and fully modified GEE can be addressed using extended quasi-likelihood methods. Alternately, standard linear modeling of singleton continuous univariate outcomes can be extended to address singleton categorical univariate outcomes.

Suggested Citation

  • George J. Knafl, 2023. "Fully Modified GEE Modeling of Correlated Univariate Outcomes," Springer Books, in: Modeling Correlated Outcomes Using Extensions of Generalized Estimating Equations and Linear Mixed Modeling, chapter 0, pages 55-72, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-41988-1_4
    DOI: 10.1007/978-3-031-41988-1_4
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