Scaled Link Functions for Heterogeneous Ordinal Response Data

This paper describes a class ordinal regression models in which the link function has scale parameters that may be estimated along with the regression parameters. One motivation is to provide a plausible model for group level categorical responses. In this case a natural class of scaled link functions is obtained by treating the group level responses as threshold averages of possible correlated latent individual level variables. We nd scaled link functions also arise naturally in other circumstances. Our methodology is illustrated through environmental risk assessment data where (correlated) individual level responses and group level responses are mixed.