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 provided for estimating correlation parameters for the directly specified exchangeable (EC), spatial autoregressive order 1 (AR1), and unstructured (UN) cases. 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. Models allowing for covariance structures based on random effects/coefficients are considered as alternatives to directly specified correlation structures.