An Explained Variation Measure for Ordinal Response Models With Comparisons to Other Ordinal R² Measures

No explained variation (R2) measure for ordinal response models enjoys wide use, and such measures have in fact received little specific attention or evaluation. To remedy this gap, the author presents and justifies R2 O, an explained variation measure for ordinal response models, which is based on a recent ordinal dispersion measure. The use and function of R2 O is illustrated, and the performance of it and other ordinal R2 measures is compared via a series of simulated sampling and variable selection experiments. The R2 O 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.