The class of CUB models: statistical foundations, inferential issues and empirical evidence
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Professors Piccolo and Simone summarize an impressive body of research dealing with CUB models and their extensions. The original ideas in Piccolo (2003) now have been extended to address the many relevant issues that one encounters in analyzing ordinal data. Our comments below reflect not so much a criticism of CUB models as reasons we’re not convinced that we should prefer this family of models over standard models that we have long used.
Our own experiences in becoming comfortable with models for analyzing ordinal data were heavily influenced by two strands of literature—Peter McCullagh’s (1980) paper and related ones on multinomial models that apply link functions to cumulative probabilities (“cumulative link models”), and Leo Goodman’s extensive work on modeling association among ordinal variables, such as summarized in Goodman (1985). An appealing aspect of both these approaches is that they fit well when it is sensible to posit underlying latent variables for which standard...
- Piccolo D (2003) On the moments of a mixture of uniform and shifted binomial random variables. Quaderni di Stat 5:85–104Google Scholar