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 are introduced in order to assess how the characteristics of the respondents may affect the ordinal score.
A review with some basic notation of this class of models are reported in the working paper Inference for CUB models: a program in R (version 4.0) with some examples concerning empirical analysis to show the usefulness and effectiveness of the proposed model. The R package CUB is now available on CRAN at https://cran.r-project.org/web/packages/CUB/index.html.
- DATASET RELGOODS
The dataset RELGOODS gathers the results of a survey aimed at measuring the evaluation of relational goods and leisure time, collected in December 2014. Every participant was asked to measure on a 10 point ordinal scale his/her personal score for several relational goods (for instance, time dedicated to friends and family, sport activity, etc) and to leisure time. In addition, the survey asked respondents to self-evaluate their level of happiness by marking a sign along a horizontal line of 110 millimeters according to their feeling, with the left-most extremity standing for “extremely unhappy”, and the right-most extremity corresponding to the status “extremely happy”. Additional details on the used ordinal scale and on the organization of the survey have been indicated as comments in the dataset file.
- DATASET EMERGENCY
A survey on the perception of metropolitan emergencies was run in Naples in four waves: participants were asked to score on a 9 point scale the degree of seriousness felt for several metropolitan issues (ranging from 1 = “completely unimportant” to 9 = “absolutely serious”). For the complete case study, see for instance Iannario-Piccolo, Metron. Additional details on the used ordinal scale and on the organization of the survey have been indicated as comments in the dataset files.
- DATASET VER
A survey on students evaluation of the Orientation services was conducted across the 13 Faculties of Università degli Studi di Napoli – Federico II in five waves: participants were asked to express their ratings on a 7 point scale (ranging from 1 = “very unsatisfied” to 7 = “extremely satisfied”). Additional details on the used ordinal scale and on the organization of the survey have been indicated as comments in the dataset file.
- DATASET OliveOil
The following dataset has been analysed in the paper M.Corduas (2014). In addition, a program written in Gauss language for fitting a bivariate Plackett distribution with CUB margins to the olive oil dataset is available for download here.