The MLC-CUB model extends the CUB (Combination of a Uniform and shifted Binomial) framework to multivariate rating data.
It assumes that each response results from two latent components:
Feeling – the respondent’s underlying attitude or preference;
Uncertainty – the indecision inherent in the response process.
By combining these components within a model-based clustering approach estimated via the EM algorithm, MLC-CUB identifies groups of respondents sharing similar patterns of feeling and uncertainty.
The figure represents the results obtained and described in the seminal paper. The participants of the study were asked to evaluate five specific aspects of the University of Naples Federico II Orientation services. Each item corresponds to a key dimension of the student experience:
Q1 – Information: Satisfaction regarding the quality and clarity of the acquired information.
Q2 – Willingness: Satisfaction regarding the availability and helpfulness of the staff.
Q3 – Office Hours: Satisfaction regarding the accessibility and convenience of the opening hours.
Q4 – Competence: Satisfaction regarding the professional expertise and knowledge of the staff.
Q5 – Global Satisfaction: An overall evaluation of the orientation service experience.
The responses were collected using a seven-point Likert scale (1 = “Very unsatisfied”, 7 = “Extremely satisfied”).
The analyses can be replicated with the code provided below.
Ventura M., Jacques J., Zuccolotto P. (2025), Model-based Clustering of Multivariate Rating Data accounting for Feeling and Uncertainty. Journal of Classification. 1-22
Ventura M., Jacques J., Zuccolotto P. (2026), Multivariate Latent Class Modeling of Rating Data for Investigating the Sustainability Perception and the Economic Behavior in the Made in Italy Sector. Statistical Papers. Submitted
Ventura, M., Jacques, J., & Zuccolotto, P. (2025). Model-Based Clustering of Multivariate Rating Data to Evaluate Consumer Perceptions on Sustainability [Short paper]. In G. Boccuzzo, E. Bovo, M. Manisera, & L. Salmaso (Eds.), IES 2025 – Statistical Methods for Evaluation and Quality (pp. 983-989). Cleup sc. ISBN: 9788854958494
Ventura, M., Jacques, J., & Zuccolotto, P. (2025). Clustering multivariate rating data within the CUB framework [Short paper]. In A. Pollice & P. Mariani (Eds.), Methodological and Applied Statistics and Demography II. SIS 2024, Short Papers, Solicited Sessions (pp. 637–642). Italian Statistical Society Series on Advances in Statistics (ISSSAS). Springer. ISBN: 9783031644467
Ventura M., Jacques J., Zuccolotto P., Sustainability and Consumer Choice: Clustering Attitudes in the Italian Furniture Market, StaTalk2025, Milan (Italy), 13-14 June 2025
Ventura M., Jaccques J., Zuccolotto P., A Mixture of Multivariate CUB Models for Clustering Rating Data, 30th Summer Working Group on Model-Based Clustering (WGMBC), Bertinoro (Italy), 22-27 July 2024.
The R package CUBClustR for fitting and validating the Multivariate Latent Class CUB (MLC-CUB) model are available together with a short user manual.
Please extract the .zip file to get the .tar.gz installation file.
To facilitate the reproduction of the results obtained in the main paper and the application of the MLC-CUB model to other multivariate rating data, an example is available for download here.
