Maximum Likelihood for Generalized Linear Model and Generalized Estimating Equations

The most frequent methods to analyze statistical data are the regression methods, whereby the maximum likelihood method or that of least squares. On the one hand, in the context of the longitudinal data or repeated measurements, these data are often unbalanced; on the other hand, their law of probability are not normal rending the passage to other models with other methods of estimate possible. In this paper, we initially recalled the maximum likelihood method applied to a mixed linear model; thereafter, we introduced the generalized estimating equations and their method of resolution. Finally, we showed the relationship between the maximum likelihood method and the iteratively reweighted least squares ones.