A new residual for ordinal outcomes.

We propose a new residual for regression models of ordinal outcomes, defined as {(,)}, where is the observed outcome and is a random variable from the fitted distribution. This new residual is a single value per subject irrespective of the number of categories of the ordinal outcome, contains directional information between the observed value and the fitted distribution, and does not require the assignment of arbitrary numbers to categories. We study its properties, describe its connections with other residuals, ranks and ridits, and demonstrate its use in model diagnostics.