Visualizing multiple results from Nonlinear CUB models with R grid Viewports


Abstract


Nonlinear CUB models have been recently introduced in the literature to model rating or ordinal data. They extend the standard CUB(Combination of Uniform and Binomial), which is a mixture modelcombining a discrete Uniform and a Shifted Binomial random variables. Unlike CUB, Nonlinear CUB models account for the unequal spacing among response categories. Nonlinear CUB can be effectively used in a variety of fields, for example whenever questionnaires with questions having ordered response categories are used to measure human perceptions and attitudes. This paper proposes a new graphical representation, which works with R grid Viewports in order to summarize multiple results from Nonlinear CUB models in a unique plot. A case study on the perceived risk in fraud management ispresented.

DOI Code: 10.1285/i20705948v8n3p360

Keywords: rating data; ordinal; feeling; uncertainty; transition probabilities; perceived risk

References


Agresti, A. (2013). Categorical Data Analysis. Wiley, New York, 3rd edition.

Capecchi, S. and Piccolo, D. (2014). Modelling the latent components of personal happiness. In Perna, C. and Sibillo, M., editors, Mathematical and Statistical Methods for

Actuarial Sciences and Finance, pages 49{52. Springer.

Corduas, M., Iannario, M., and Piccolo, D. (2009). A class of statistical models for evaluating services and performances. In Monari, P., Bini, M., Piccolo, D., and Salmaso, L., editors, Statistical methods for the evaluation of educational services and quality of products, pages 99{117. Springer.

D'Elia, A. (2008). A statistical modelling approach for the analysis of tmd chronic pain data. Stat Methods Med Res, 17:389{403.

D'Elia, A. and Piccolo, D. (2005). A mixture model for preference data analysis. Comput Stat Data An, 49:917{934.

Gambacorta, R. and Iannario, M. (2013). Measuring job satisfaction with CUB models. Labour, 27:198{224.

Gambacorta, R., Iannario, M., and Vallian, R. (2014). Design-based inference in a mixture model for ordinal variables for a two stage stratied design. Aust NZ J Stat, 56:125{143.

Grilli, L., Iannario, M., Piccolo, D., and Rampichini, C. (2013). Latent class CUB models. Adv Data Anal Classif, 8:105{119.

Iannario, M. (2012a). Hierarchical CUB models for ordinal variables. Commun Stat-Theor M, 41:3110{3125.

Iannario, M. (2012b). Modelling shelter choices in a class of mixture models for ordinal responses. Stat Method Appl, 20:1{22.

Iannario, M. (2012c). CUBE models for interpreting ordered categorical data with overdispersion. Quad Stat, 14:137{140.

Iannario, M. (2014). Modelling uncertainty and overdispersion in ordinal data. Commun Stat-Theor M, 43:771{786.

Iannario, M., Manisera, M., Piccolo, D., and Zuccolotto, P. (2012). Sensory analysis in the food industry as a tool for marketing decisions. Adv Data Anal Classif, 6:303{321.

Iannario, M. and Piccolo, D. (2010). A new statistical model for the analysis of customer satisfaction. Qual Technol Quantit Manag, 7:149{168.

Iannario, M. and Piccolo, D. (2012). CUB models: Statistical methods and empirical evidence. In Kenett, R. S. and Salini, S., editors, Modern Analysis of Customer Surveys, pages 231{258. Wiley, New York.

Iannario, M. and Piccolo, D. (2014). A Short Guide to CUB 3.0 Program. Available at

https://www.researchgate.net/publication/260959050.

Manisera, M. and Zuccolotto, P. (2013). Nonlinear CUB models: some stylized facts. QdS - J Methodol Appl Statist, 1{2.

Manisera, M. and Zuccolotto, P. (2014a). Modeling don't know" responses in rating scales. Pattern Recogn Lett, 45:226{234.

Manisera, M. and Zuccolotto, P. (2014b). Modeling rating data with Nonlinear CUB models. Comput Stat Data An, 78:100{118.

Manisera, M. and Zuccolotto, P. (2015a). Numerical optimization and EM algorithm in a mixture model for human perceptions analysis. Working paper.

Manisera, M. and Zuccolotto, P. (2015b). On the identiability of Nonlinear CUB models. Working paper.

Manisera, M. and Zuccolotto, P. (2015c). Nonlinear CUB models: the R program. Working paper.

Manisera, M. and Zuccolotto, P. (2015d). Treatment of `don't know' responses in a mixture model for rating data. Working paper.

Murrell, P. (1999). Layouts: A mechanism for arranging plots on a page. J Comput Graph Stat, 8:121{134.

Piccolo, D. (2003). On the moments of a mixture of uniform and shifted binomial random variables. Quad Stat, 5:85{104.

Piccolo, D. (2006). Observed information matrix for MUB models. Quad Stat, 8:33{78.

Piccolo, D. (2014). Inferential issues on CUBE models with covariates. Commun Stat- Theor M, 43.

Piccolo, D. and D'Elia, A. (2008). A new approach for modelling consumers' preferences. Food Qual Prefer, 19:247{259.

Tutz, G. (2012). Regression for categorical data. Cambridge University Press, Cambridge.


Full Text: pdf
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.