D’Elia A., Piccolo D. (2005), A mixture model for preferences data analysis. Computational Statistics & Data Analysis, 49(3), 917-934.
A mixture model for preferences data, which adequately represents the composite nature of the elicitation mechanism in ranking processes, is proposed. Both probabilistic features of the mixture distribution and inferential and computational issues arising from the maximum likelihood parameters estimation are addressed. Moreover, empirical evidence from different data sets confirming the goodness of fit of the proposed model to many real preferences data is shown.
Piccolo D., Simone R. (2019). The class of cub models: statistical foundations, inferential issues and empirical evidence. Statistical Methods & Applications, 28(3), 389-435.
This paper discusses a general framework for the analysis of rating and preference data that is rooted on a class of mixtures of discrete random variables. These models have been extensively studied and applied in the last 15 years thanks to a flexible and parsimonious parametrization of data generating process and to prompt interpretation of results. The approach considers the final response as the combination of feeling and uncertainty, by allowing for finer model specifications to include refuge options, response styles and possible overdispersion, also in relation to subjects’ and objects’ covariates. The article establishes the state of art of the research inherent to this paradigm, in terms of methodology, inferential procedures and fitting measures, by emphasizing capabilities and limitations yet establishing new findings. In particular, explicative power and predictive performances of cub statistical models for ordinal data are examined and new topics that could boost and support the modelling of uncertainty in this framework are provided. Possible developments are outlined throughout the whole presentation and final comments conclude the paper.
Rejoinder to the discussion by Domenico Piccolo & Rosaria Simone (477-493)
A Python implementation of CUB models is available via PyPI, with open-source code maintained on Massimo Pierini (MaxDevBlock) GitHub profile.
by Domenico Piccolo
(Workshop “Statistical Methods and Models for Ordinal Data”, University of Brescia, 25 May 2023)
Includes animated slides (slides 9–11) illustrating key concepts.
