Inferential Issues on CUBE Models with Covariates

Abstract

We introduce cube models with covariates, a class of discrete mixture distributions able to take uncertainty and overdispersion of ordinal data into account. The main result of the paper concerns the analytical derivation of the observed variance–covariance matrix of this model, a necessary step for the asymptotic inference about estimated parameters and model validation. We emphasize some computational aspects of the procedure and discuss the usefulness of the approach on a real case study.