Analyzing coarsened categorical data with or without probabilistic information

In some applications, only a coarsened version of a categorical outcome variable can be observed. Parametric inference based on the maximum likelihood approach is feasible in principle, but it cannot be covered computationally by standard software tools. In this article, we present two commands facilitating maximum likelihood estimation in this situation for a wide range of parametric models for categorical outcomes-in the cases both of a nominal and an ordinal scale. In particular, the case of probabilistic information about the possible values of the outcome variable is also covered. Two examples motivating this scenario are presented and analyzed.