Modelling shelter choices in a class of mixture models for ordinal responses

Cognitive Dissonance in the Self-assessed Health in Brazil: A CUB Model Analysis Using 2013 National Health Survey Data

This study ai ms to verify and analyze the existence of cognitive dissonance in the self-assessment of health by individuals in Brazil, that is, the difference between self-rated health and the health status of individuals. To accomplish this, we use data from the 2013 National Health Survey, which collected the self-assessments that individuals made of their health and information about their health status. This information was used to build indices that seek to represent a person's health status in relation to chronic illnesses, physical and mental well-being, eating habits and lifestyle. To identify the presence of cognitive dissonance, the CUB (Combination of a discrete Uniform and shifted Binomial distributions) model was used, which relates self-assessed health with the developed indices. Cognitive dissonance was identified in self-assessed health in relation to eating habits and lifestyle, and this dissonance may be associated with a present bias in the self-assessment of health in Brazil.

Analysing sport data with clusters of opposite preferences

In the analysis of questionnaire-based evaluation of sport preferences, measurements of sport participation, opinions on social implications such as resurgence of racism, violence in stadiums and doping, the need arises to establish connections among motivations, subjects’ characteristics and responses. In this setting, the article deals with a selection of statistical models suitable to analyse sport rating data in which clusters of opposite responses are observed. Specifically, a two-component mixture of inverse hypergeometric (MIHG) distributions will be introduced and tested against competing models in order to yield a multifold interpretation of results. The ultimate comparative analysis will consider discrete models with a specific focus on those accounting for both uncertainty and feeling of self-evaluation in presence of inflation at the extreme categories. After a brief review of the methods, the proposal will be discussed both on ranking and rating data on the basis of two surveys on sport preferences and on measurements of sport activity: the identification of clusters of respondents with opposite choices will be investigated also in terms of covariates by comparing fitting performances of the selected models. The conclusions and insights offered by the study can be exploited to design plans of action for some specific policy or marketing strategy.

A class of mixture models for multidimensional ordinal data

In rating surveys, people are requested to express preferences on several aspects related to a topic by selecting a category in an ordered scale. For such data, we propose a model defined by a mixture of a uniform distribution and a Sarmanov distribution with CUB (combination of uniform and shifted binomial) marginal distributions ( D'Elia and Piccolo, 2005 ). This mixture generalizes the CUB model to the multivariate case by taking into account the association among answers of the same individual to the items of a questionnaire. It also allows us to distinguish two kinds of uncertainty: specific uncertainty, related to the indecision for single items, and global uncertainty referred to the respondent's hesitancy in completing the whole questionnaire. A simulation and a real case study highlight the usefulness of the new methodology.

Analyzing bivariate ordinal data with CUB margins

Statistical modelling for ordinal data has received a considerable attention in the literature, and a consolidated theory relying on Generalized Linear Model approach has been developed. In this article, we present an innovative technique for modelling bivariate ordinal data. In particular, we consider the method introduced by Plackett for constructing a one-parameter bivariate distribution from given margins, and we apply it in order to represent correlated ordinal variables which individually follows a CUB model. This is a univariate mixture distribution defined by the convex Combination of a Uniform and a shifted Binomial distribution whose parameters may be related to rater's covariates. The article shows how the bivariate distribution can be defined and how its characterizing parameter, which describes the association between the component random variables, can be related to the subject's covariates. The proposed approach is applied to the study of two key drivers of extra virgin olive oil consumption in Italy. The technique allows a representation of the data whose meaning can be easily interpreted providing useful information for management support.