A model for correlated binary data is presented. Marginal probabilities and odds ratios are allowed to have general regression structures that include multiple classes and multiple levels of nesting. Estimation is done through the generalized estimating equations approach of Liang and Zeger (1986, Biometrika 73, 13-22). They are contrasted with conditional models and recommendations for choosing between the two are given. Examples from genetic epidemiology are presented.