Modelling uncertainty and response styles in ordinal data

On finite mixtures of Discretized Beta model for ordered responses

The paper discusses the specification of finite mixture models based on the Discretized Beta distribution for the analysis of ordered discrete responses, as ratings and count data. The ultimate goal of the paper is to parameterize clusters of opposite and intermediate response outcomes. After a thorough discussion on model interpretation, identifiability and estimation, the proposal is illustrated on the wake of a case study on the probability to vote for German Political Parties and with a comparative discussion with the state of the art.

Uncertainty in Latent Trait Models

A model that extends the Rasch model and the Partial Credit Model to account for subject-specific uncertainty when responding to items is proposed. It is demonstrated that ignoring the subject-specific uncertainty may yield biased estimates of model parameters. In the extended version of the model, uncertainty and the underlying trait are linked to explanatory variables. The parameterization allows to identify subgroups that differ in uncertainty and the underlying trait. The modeling approach is illustrated using data on the confidence of citizens in public institutions.

Modeling different behaviors in disclosing risk perception

In many fields, people are requested to express their level of awareness about some risk (mainly associated with health, environment, energy, etc.) by selecting a category in an ordered scale. We propose a model for such ordinal data by taking into account that the observed response does not necessarily reflect the respondent's true opinion since the final answer can be inaccurate or completely random. The proposed model hypothesizes three behaviors in the process of answering: accurate interviewees express their risk perception exactly, uncertain ones randomly select the response according to the uniform distribution, and inaccurate interviewees make evaluation errors but with high probability they choose a rating close to the true one. Statistical inference for the proposed models is addressed without assuming that the model, to be fitted, is correctly specified. Two real case studies on the awareness of geo-hydrological risk and work-related stress risk are considered using the proposed methodology.

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.