R/CUB_package.R

In CUB: A Class of Mixture Models for Ordinal Data

#' @title CUB package
#' @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.\cr
#'  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.\cr
#'   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 model) 
#'   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. \cr
#'   CUB models have been firstly introduced by Piccolo (2003) and implemented on real datasets concerning ratings and rankings 
#'   by D'Elia and Piccolo (2005), Iannario and Piccolo (2012).\cr
#'   The CUB package allows the user to estimate and test CUB models and their extensions by using maximum 
#'   likelihood methods. The package covers the main models of the class of Generalized Mixture Models with uncertainty 
#'   (GEM - Iannario and Piccolo (2016a)), a comprehensive framework for modelling ordinal data. The accompanying vignettes 
#'   supplies the user with detailed usage instructions and examples. \cr
#'  Acknowledgements: The Authors are grateful to Maria Antonietta Del Ferraro, Francesco Miranda and
#'   Giuseppe Porpora for their preliminary support in the implementation of the first version of the package.
#' @details 
#'   \tabular{ll}{
#' Package: \tab CUB\cr
#' Type: \tab Package\cr
#' Version: \tab 1.1.4\cr
#' Date: \tab 2017-10-11\cr
#' License: GPL-2 | GPL-3
#'  }
#' @source  \url{http://www.labstat.it/home/research/resources/cub-data-sets-2/}
#' @author  Maria Iannario, Domenico Piccolo, Rosaria Simone
#' @references  D'Elia A. (2003). Modelling ranks using the inverse hypergeometric distribution, 
#' \emph{Statistical Modelling: an International Journal}, \bold{3}, 65--78 \cr
#' Piccolo D. (2003). On the moments of a mixture of uniform and shifted binomial random variables,
#'  \emph{Quaderni di Statistica}, \bold{5}, 85--104 \cr 
#'   D'Elia A. and Piccolo D. (2005).  A mixture model for preferences data analysis, 
#'   \emph{Computational Statistics & Data Analysis},  \bold{49}, 917--937 \cr
#' Capecchi S. and Piccolo D. (2017). Dealing with heterogeneity in ordinal responses,
#'  \emph{Quality and Quantity}, \bold{51}(5), 2375--2393 \cr
#'   Iannario M. and Piccolo D. (2016a). A comprehensive framework for regression models of ordinal data.
#'    \emph{Metron}, \bold{74}(2), 233--252.\cr
#'    Iannario M. and Piccolo D. (2016b). A generalized framework for modelling ordinal data. 
#'  \emph{Statistical Methods and Applications}, \bold{25}, 163--189.\cr 
#' @name CUB_package 
#' @keywords package
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