Latent class CUB models

The paper proposes a latent class version of Combination of Uniform and (shifted) Binomial random variables (CUB) models for ordinal data to account for unobserved heterogeneity. The extension, called LC-CUB, is useful when the heterogeneity is originated by clusters of respondents not identified by covariates: this may generate a multimodal response distribution, which cannot be adequately described by a standard CUB model. The LC-CUB model is a finite mixture of CUB models yielding a multimodal theoretical distribution. Model identification is achieved by constraining the uncertainty parameters to be constant across latent classes. A simulation experiment shows the performance of the maximum likelihood estimator, whereas the usefulness of the approach is illustrated by means of a case study on political self-placement measured on an ordinal scale.