Abstract. This paper focuses on marginal regression models for correlated binary responses when estimation of the association structure is of primary interest. A new estimating function approach based on orthogonalized residuals is proposed. A special case of the proposed procedure allows a new representation of the alternating logistic regressions method through marginal residuals. The connections between second-order generalized estimating equations, alternating logistic regressions, pseudo-likelihood and other methods are explored. Efficiency comparisons are presented, with emphasis on variable cluster size and on the role of higher-order assumptions. The new method is illustrated with an analysis of data on impaired pulmonary function.