A modified version of alternating logistic regressions (ALR) with estimation based on orthogonalized residuals (ORTH) is implemented, which use paired estimating equations to jointly estimate parameters in marginal mean and within-association models. The within-cluster association between ordinal responses is modeled by global pairwise odds ratios (POR). A finite-sample bias correction is provided to POR parameter estimates based on matrix multiplicative adjusted orthogonalized residuals (MMORTH) for correcting estimating equations, and different bias-corrected variance estimators such as BC1, BC2, and BC3.