cubm package in R to fit CUB models



Palabras clave:

CUB models, Feeling and uncertainty, Ordinal data, R.


The class of CUB models is commonly used by practitioners to model ordinal data, in this paper we propose the cubm package which provides the class of CUB models in the R system for statistical computing. The cubm package allows to specify a formula for each parameter of the model, the Maximum Likelihood (ML) estimation is performed by optimization via the functions nlminb, optim and DEoptim and the variance-covariance matrix can be obtained by numerical approximation of the Hessian matrix or by bootstrap method. The utility of the package is illustrated by an application and a simulation study.

Biografía del autor/a

, Universidad Nacional de Colombia

Doctor en Ciencias por la Universidad de São Paulo (USP, 2013) en São Paulo, Brasil. Magíster en Estadística de la Universidad Nacional de Colombia (UNAL, 2007) e Ingeniero Industrial por la Universidad Industrial de Santander (UIS, 2002) en Bucaramanga, Colombia. Entre los intereses de investigación se encuentran la estadística computacional, modelos de regresión y técnicas de comparaciones múltiples. Miembro de la Comunidad de Investigación de Operaciones Medellín, miembro del comité editorial de la Revista de Ingeniería Industrial UPB y miembro de Statistical Modelling Society.


Arboretti, R. & Bordignon, P. (2016), ‘Consumer preferences in food packaging: Cub models and conjoint analysis’, British Food Journal 118(3), 527-540.

Ardia, D., Boudt, K., Carl, P., Mullen, K. M. & Peterson, B. G. (2011), ‘Differential Evolution with DEoptim: An application to non-convex portfolio optimization’, The R Journal 3(1), 27-34.

Boatto, V., Rossetto, L., Bordignon, P., Arboretti, R., Salmaso, L., Griffith, C. & Griffith, C. (2016), ‘Cheese perception in the north american market: empirical evidence for domestic vs. imported parmesan’, British Food Journal 118(7).

Cafarelli, B. & Crocetta, C. (2016), An evaluation of the student satisfaction based on cub models, in ‘Topics in Theoretical and Applied Statistics’, Springer, pp. 73-83.

Capecchi, S. (2015), ‘Modelling the perception of conflict in working conditions’, Electronic Journal of Applied Statistical Analysis 8(3), 298-311.

Capecchi, S. & Piccolo, D. (2014), Modelling the latent components of personal happiness, in ‘Mathematical and Statistical Methods for Actuarial Sciences and Finance’, Springer, pp. 49-52.

Corduas, M. (2011), Assessing similarity of rating distributions by kullback-leibler divergence, in ‘Classification and Multivariate Analysis for Complex Data Structures’, Springer, pp. 221-228.

D’Elia, A. & Piccolo, D. (2005), ‘A mixture model for preference data analysis’, Computational Statistics Data Analysis 49(3), 917-934.

Gambacorta, R. & Iannario, M. (2013), ‘Measuring job satisfaction with cub models’, Labour 27(2), 198-224.

Gambacorta, R., Iannario, M. & Valliant, R. (2014), ‘Design-based inference in a mixture model for ordinal variables for a two stage stratified design’, Australian & New Zealand Journal of Statistics 56(2), 125-143.

Gilbert, P. & Varadhan, R. (2016), numDeriv: Accurate Numerical Derivatives. R package version 2016.8-1.*

Grilli, L., Iannario, M., Piccolo, D. & Rampichini, C. (2014), ‘Latent class cub models’, Advances in Data Analysis and Classification 8(1), 105-119.

Iannario, M. (2008), ‘Dummy covariates in cub models’, Statistica 68(2), 179-200.

Iannario, M. (2010), ‘On the identifiability of a mixture model for ordinal data’, Metron 68(1), 87-94.

Iannario, M. (2012), ‘Hierarchical cub models for ordinal variables’, Communications in Statistics-Theory and Methods 41(16-17), 3110-3125.

Iannario, M. (2014), ‘Modelling uncertainty and overdispersion in ordinal data’, Communications in Statistics-Theory and Methods 43(4), 771-786.

Iannario, M., Manisera, M., Piccolo, D. & Zuccolotto, P. (2012), ‘Sensory analysis in the food industry as a tool for marketing decisions’, Advances in Data Analysis and classification 6(4), 303-321.

Iannario, M. & Piccolo, D. (2010), ‘A new statistical model for the analysis of customer satisfaction’, Quality Technology & Quantitative Management 7(2), 149-168.

Iannario, M. & Piccolo, D. (2012), ‘Cub models: Statistical methods and empirical evidence’, Modern Analysis of Customer Surveys pp. 231-258.

Iannario, M. & Piccolo, D. (2015), ‘A generalized framework for modelling ordinal data’, Statistical Methods & Applications pp. 1-27.

Iannario, M., Piccolo, D. & Simone, R. (2016), CUB: A Class of Mixture Models for Ordinal Data. R package version 1.0. *

Innario, M. (2012), ‘Cube models for interpreting ordered categorical data with overdispersion’, Quaderni di statistica 14(14), 137-140.

Manisera, M. & Zuccolotto, P. (2013), ‘Nonlinear cub models: some stylized facts’,Quaderni di Statistica 15, 111-130.

Manisera, M. & Zuccolotto, P. (2014), ‘Modeling rating data with nonlinear cub models’, Computational Statistics & Data Analysis 78, 100-118.

Manisera, M. & Zuccolotto, P. (2015), ‘Visualizing multiple results from nonlinear cub models with r grid viewports’, Electronic Journal of Applied Statistical Analysis 8(3), 360-373.

Manisera, M. & Zuccolotto, P. (2016), ‘Treatment of "don’t knowresponses in a mixture model for rating data’, METRON 74(1), 99-115.

McLachlan, G. & Krishnan, T. (1997), ‘The em algorithm and extensions’.

Mullen, K., Ardia, D., Gil, D., Windover, D. & Cline, J. (2011), ‘DEoptim: An R package for global optimization by differential evolution’, Journal of Statistical Software 40(6), 1-26. *

Oberski, D. & Vermunt, J. (2015), ‘The cub model and its variations are restricted loglinear latent class models’, EJASA .

Piccolo, D. (2003a), ‘Computational issues in the em algorithm for ranks model estimation with covariates’, Quaderni di Statistica 5, 1-22.

Piccolo, D. (2003b), ‘On the moments of a mixture of uniform and shifted binomial random variables’, Quaderni di Statistica 5(1), 85-104.

Piccolo, D. (2015), ‘Inferential issues on cube models with covariates’, Communications in Statistics-Theory and Methods 44(23), 5023-5036.




Cómo citar

Freddy Hernández, Olga Cecilia, & Sebastián. (2018). cubm package in R to fit CUB models. Comunicaciones En Estadística, 11(2), 219–238.