Generalized Models for Binary and Ordinal Responses

Abstract

In a statistical information theoretical setup, the logistic regression model has been extended to a generalized family of binary regression models that are scaled through the $\phi$-divergence [8]. Here, we introduce generalized families of models for ordinal responses. Such families of generalized models, though flexible, have not easily interpretable parameters. We propose simple measures that facilitate a straightforward interpretation for the effects of explanatory variables on a binary or ordinal response.