In this paper, a new discrete statistical model for ordered categorical data is proposed via fixed-point discretization of a beta latent variable. The resulting discretized beta distribution has a highly flexible shape and it can be either over-dispersed or under-dispersed with respect to the binomial distribution. It has only two parameters, which may therefore parsimoniously depend on covariates and on random effects, providing new tools for the analysis of structured, clustered or longitudinal ordinal data. Practical examples and advices are given and an application of the new model to subjective evaluations of a gastrointestinal disease is shown.