Multilevel Latent Class with CUB Models

We propose a latent class model for ordinal data with CUB (combination of discrete uniform and shifted binomial) distributions in the case of multilevel structures of the data. The CUB model is a powerful approach to the analysis of ordinal data, where the elicitation process is thought to be governed by a feeling parameter and an uncertainty parameter. Ordinal data are common across different research fields and may present a multilevel structure with units nested within groups. The model we present extends the framework of multivariate CUB models for model-based clustering to multilevel data, either hierarchical or cross-classified. Numerical experiments on simulated data highlight the added value of assuming a CUB model to account for ordinal information; the procedure's interest is also shown through a real data application.