 Population-averaged logistic model for repeated binary outcomes

For independent subjects with repeated Bernoulli observations, specify marginal means $m_{ij}={\mathrm{logit}}^{-1}(w_{ij}^T\gamma )$. A generalized estimating equation uses their derivative matrix $D_i$ and working covariance matrix $V_i$ to solve ${\sum }_i{D}_i^T{V}_i^{-1}(Y_i-m_i)=0$. Subject-level sandwich covariance matrices give robust uncertainty when the mean is correctly specified but the working correlation is not. The coefficients describe population odds ratios; this mean specification does not prescribe a complete joint distribution within a subject.