Assessment of Regression Models With Discrete Outcomes Using Quasi-Empirical Residual Distribution Functions

Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard assessment tools such outcomes (e.g., deviance residuals) often show a large discrepancy from the hypothesized pattern even under true and are not informative, especially when data highly binary). To fill this gap, we propose quasi-empirical residual distribution function general ordinal count) that serves as alternative to empirical of Cox–Snell residuals. The tool is principled approach does require injecting noise into data. When at least one continuous covariate available, asymptotically proposed converges uniformly identity correctly specified model, Through simulation studies, demonstrate empirically outperforms commonly used residuals various tasks, since it close significantly departs misspecification, thus effective tool. Supplementary materials article available online.