ORTH: R and SAS Software For Correlated Binary Data Based On Orthogonalized

In this article, we describe a new software for modelling correlated binary data whose raison d’etre is based on the work of Zink (Zink, 2003). The approach taken is based on what Zink calls“orthogonalized residuals ” that includes, as a special case, alternating logistic regres-sions(Carey et al., 1993). The use of these residuals leads to a feasi-ble computational platform for correlated binary data that addresses some of the shortcomings of an earlier formulation based on condi-tional residuals. Furthermore, this new approach recasts alternating logistic regressions in a framework consistent with standard estimat-ing equation theory facilitating study of its properties. The software is flexible with respect to fitting in that the user can choose estimat-ing equations for the association model based on alternating logistic regressions or orthogonalized residuals, the latter choice providing a non-diagonal working covariance matrix for second moment parame-ters for obtaining potentially greater efficiency. Diagnostics based on this method are also implemented in the software. The mathemati-cal details of the procedure are briefly reviewed and the software is applied to medical data sets. 1