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.
Two-Component Mixture Model in the Presence of Covariates
