Comments on The class of cub models: statistical foundations, inferential issues and empirical evidence by D. Piccolo and R. Simone
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I want to congratulate the authors on a comprehensive and stimulating overview on the class of CUB models. The approach was developed about a decade ago, with Domenico Piccolo as the leading researcher in the area. The approach turned out to be very fruitful, various extensions and versions of the basic CUB model have been given since then. I confine myself to some brief remarks with a focus on potential areas of future research.
CUB models as structured mixture models
CUB models are discrete mixture models, they assume that what one can observe is the result of a mixture of unobserved responses. Mixture models are strong tools but challenging with regard to estimation and interpretation. It is not uncommon that data analysts fit a mixture of an unknown number of regression or latent trait models without constraints on the mixture components, that is, regression coefficients and dispersion parameters in the components can vary freely. After fitting various models one selects...