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Extended Linear Mixed 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

Extended linear mixed modeling (ELMM) is based on full maximum likelihood estimation, maximizing the likelihood in the correlation parameters as well as in the mean and dispersion parameters. Revised formulations are provided for estimating equations, gradient vectors, and Hessian matrices. Adjustments to the estimation process are provided. Formulations are also provided for estimating exchangeable (EC), spatial autoregressive order 1 (AR1), and unstructured (UN) correlation parameters. The formulations for the EC and spatial AR1 cases provide for efficient correlation parameter estimation without storing associated correlation matrices. How to verify gradient and Hessian formulations and their software implementations is addressed. Direct variance modeling is defined, using only general dispersions to model variances rather than using extended variance modeling also considering distribution-specific variances based on the means.

Suggested Citation

  • George J. Knafl, 2023. "Extended Linear Mixed Modeling of Correlated Univariate Outcomes," Springer Books, in: Modeling Correlated Outcomes Using Extensions of Generalized Estimating Equations and Linear Mixed Modeling, chapter 0, pages 73-99, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-41988-1_5
    DOI: 10.1007/978-3-031-41988-1_5
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