A generalized framework for modelling ordinal data

• Published in: Statistical methods & applications Vol. 25; no. 2; pp. 163 - 189
• Main Authors: Iannario, Maria, Piccolo, Domenico
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2016; Springer Nature B.V
• Subjects: Applied mathematics; Asymptotic methods; Asymptotic properties; Business; Case studies; Chemistry and Earth Sciences; Computer Science; Computer simulation; Consistency; Data analysis; Economics; Experiments; Finance; Generalized linear models; Health Sciences; Humanities; Insurance; Law; Management; Mathematics and Statistics; Maximum likelihood method; Medicine; Physics; Polls & surveys; Preferences; Probability; Random variables; Shelters; Simulation; Sociology; Statistical analysis; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; models; choices; Rating survey; Ordinal data
• ISSN: 1618-2510; 1613-981X
• DOI: 10.1007/s10260-015-0316-9

In several applied disciplines, as Economics, Marketing, Business, Sociology, Psychology, Political science, Environmental research and Medicine, it is common to collect data in the form of ordered categorical observations. In this paper, we introduce a class of models based on mixtures of discrete random variables in order to specify a general framework for the statistical analysis of this kind of data. The structure of these models allows the interpretation of the final response as related to feeling, uncertainty and a possible shelter option and the expression of the relationship among these components and subjects’ covariates. Such a model may be effectively estimated by maximum likelihood methods leading to asymptotically efficient inference. We present a simulation experiment and discuss a real case study to check the consistency and the usefulness of the approach. Some final considerations conclude the paper.