CUB_package: A Class of Mixture Models for Ordinal Data
Description
The analysis of human perceptions is often carried out by resorting to questionnaires,
where respondents are asked to express ratings about the items being evaluated. The standard goal of the
statistical framework proposed for this kind of data (e.g. cumulative models) is to explicitly characterize
the respondents' perceptions about a latent trait, by taking into account, at the same time,
the ordinal categorical scale of measurement of the involved statistical variables. The new class of models
starts from a particular assumption about the unconscious mechanism leading individuals' responses
to choose an ordinal category on a rating scale. The basic idea derives from the awareness that two latent
components move the psychological process of selection among discrete alternatives: attractiveness
towards the item and uncertainty in the response. Both components of models concern the stochastic
mechanism in term of feeling, which is an internal/personal movement of the subject towards the item,
and uncertainty pertaining to the final choice.
Thus, on the basis of experimental data and statistical motivations, the response distribution is modelled
as the convex Combination of a discrete Uniform and a shifted Binomial random variable (denoted as CUB models)
whose parameters may be consistently estimated and validated by maximum likelihood inference.
In addition, subjects' and objects' covariates can be included in the model in order to assess how the
characteristics of the respondents may affect the ordinal score.
CUB models have been firstly introduced by Piccolo (2003) and implemented on real datasets by D'Elia
and Piccolo (2005), Iannario and Piccolo (2012).
The CUB package allows the user to estimate and test CUB models and their extensions by using maximum
likelihood methods.
ACKNOWLEDGEMENTS: The Authors are grateful to Maria Antonietta Del Ferraro, Francesco Miranda and
Giuseppe Porpora for their support in the implementation of the package.
Details
|
Package: |
| CUB |
|
Type: |
| Package |
|
Version: |
| 0.1 |
|
Date: |
| 2016-6-7 |
References
Piccolo D. (2003). On the moments of a mixture of uniform and shifted binomial random variables,
Quaderni di Statistica, 5, 85--104 D'Elia A. and Piccolo D. (2005).
A mixture model for preferences data analysis, Computational Statistics & Data Analysis,
49, 917--937
Iannario M. and Piccolo D. (2012). CUB models: Statistical methods and empirical evidence, in:
Kenett R. S. and Salini S. (eds.), Modern Analysis of Customer Surveys: with applications using R,
J. Wiley and Sons, Chichester, 231--258
Iannario M. and Piccolo D. (2014). Inference for CUB models: a program in R,
Statistica & Applicazioni, XII n.2, 177--204