Generalized linear mixed model with Bayesian rank likelihood

We consider situations where a model for an ordered categorical response variable is deemed necessary. Standard models may not be suited to perform this analysis, being that the marginal probability effects to a large extent are predetermined by the rigid parametric structure. We propose to use a rank likelihood approach in a non Gaussian framework and show how additional flexibility can be gained by modeling individual heterogeneity in terms of latent structure. This approach avoids to set a specific link between the observed categories and the latent quantities and it is discussed in the broadly general case of longitudinal data. A real data example is illustrated in the context of sovereign credit ratings modeling and forecasting.