Marginal regression models are an extension of the usual Generalized Linear Model (GLM; McCullagh and Nelder, 1989) to the case of correlated data. Beginning with the stimulating paper of Liang and Zeger (1986) a lot of methods for handling correlated data were proposed. The Generalized Estimating Equations approach of Liang and Zeger (1986) is a semiparametric quasi-likelihood approach for correlated data using the correlation as a measure of association. It was extended to several measures for the association and several methods for estimating the parameters. An overview of these methods is given e.g. by Ziegler, A., Kastner, C., Grömping, U., Blettner, M. (1996), or Fahrmeir and Tutz (1994).
Full likelihood methods are another approach to estimate marginal models. They are useful, if there are only few observations per sample unit. In this case they are an flexible tool for modeling the marginal distributions and the association, simultaneously. The case of binary response was introduced by Fitzmaurice and Laird (1993). A generalization to multicategorical data is given by Heumann, C. (1996).
These methods have found a wide acceptance in the literature, and a lot of examples and simulations show that these methods are applicable in practice. There is software available for these methods, e.g. the Splus macro `gee' by Carey and McDermott or a SAS macro from Karim and Zeger, but these and other programs comply only partially with our requirements for user friendly software:
Literature:
Fahrmeir, L. and Tutz, G., 1994: Multivariate statistical modelling based on generalized linear models, New York: Springer
Kastner, C., Fieger, A. and Heumann, C., 1996: MAREG and WINMAREG - a tool for marginal regression models, Statistical Software Newsletter in Computational Statistics and Data Analysis 24, 237-241
McCullagh, P. and Nelder, J., 1989: Generalized linear models, 2nd ed. London: Chapman & Hall