An Explained Variation Measure for Ordinal Response Models With Comparisons to Other Ordinal R ² Measures

Abstract

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.