An explained variation measure for ordinal response models with comparisons to other ordinal R2 measures

No explained variation (R-2) measure for ordinal response models enjoys wide use, and such measures have infact received little specific attention or evaluation. To remedy this gap, the author presents and justifies R-O(2), an explained variation measure for ordinal response models, which is based on a recent ordinal dispersion measure. The use and function of R-O(2) is illustrated, and the performance of it and other ordinal R-2 measures is compared via a series of simulated sampling and variable selection experiments. The R-O(2) and a bias-adjusted version of it perform well in the simulation experiments and have a number of other advantages that make them attractive as measures of fit for any ordinal response model.