ORTH: R and SAS software for regression models of correlated binary data based on orthogonalized residuals and alternating logistic regressions

This article describes a new software for modeling correlated binary data based on orthogonalized residuals, a recently developed estimating equations approach that includes, as a special case, alternating logistic regressions. The software is flexible with respect to fitting in that the user can choose estimating equations for association models based on alternating logistic regressions or orthogonalized residuals, the latter choice providing a non-diagonal working covariance matrix for second moment parameters providing potentially greater efficiency. Regression diagnostics based on this method are also implemented in the software. The mathematical background is briefly reviewed and the software is applied to medical data sets.