Affiliation:
1. Department of Statistics, University of Washington, Seattle, WA 98195, USA
2. Department of Statistics, University of California, Davis, CA 95616, USA
Abstract
Individual subjects’ ratings neither are metric nor have homogeneous meanings, consequently digital- labeled collections of subjects’ ratings are intrinsically ordinal and categorical. However, in these situations, the literature privileges the use of measures conceived for numerical data. In this paper, we discuss the exploratory theme of employing conditional entropy to measure degrees of uncertainty in responding to self-rating questions and that of displaying the computed entropies along the ordinal axis for visible pattern recognition. We apply this theme to the study of an online dataset, which contains responses to the Rosenberg Self-Esteem Scale. We report three major findings. First, at the fine scale level, the resultant multiple ordinal-display of response-vs-covariate entropy measures reveals that the subjects on both extreme labels (high self-esteem and low self-esteem) show distinct degrees of uncertainty. Secondly, at the global scale level, in responding to positively posed questions, the degree of uncertainty decreases for increasing levels of self-esteem, while, in responding to negative questions, the degree of uncertainty increases. Thirdly, such entropy-based computed patterns are preserved across age groups. We provide a set of tools developed in R that are ready to implement for the analysis of rating data and for exploring pattern-based knowledge in related research.
Subject
General Physics and Astronomy
Reference19 articles.
1. Goodman, L.A. (1978). Log-linear Models and Latent Structure Analysis, Wheeler Hall.
2. Agresti, A. (2003). Categorical Data Analysis, John Wiley & Sons.
3. Analyzing ordinal data with metric models: What could possibly go wrong?;Liddell;J. Exp. Soc. Psychol.,2018
4. R Core Team (2021). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Available online: https://www.R-project.org/.
5. Rosenberg, M. (1965). Society and the Adolescent Self-Image, Princeton University Press.