Furfaro Emanuela, Hsieh Fushing
Department of Statistics, University of Washington, Seattle, WA 98195, USA.
Department of Statistics, University of California, Davis, CA 95616, USA.
Entropy (Basel). 2023 Sep 8;25(9):1311. doi: 10.3390/e25091311.
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.
个体受试者的评分既不是度量值，其含义也不具有同质性，因此，以数字标记的受试者评分集合本质上是有序的和分类的。然而，在这些情况下，文献中更倾向于使用针对数值数据设计的度量方法。在本文中，我们讨论了两个探索性主题：一是采用条件熵来度量对自评问题回答中的不确定性程度；二是将计算出的熵值沿有序轴显示，以便进行可见模式识别。我们将这一主题应用于一个在线数据集的研究，该数据集包含对罗森伯格自尊量表的回答。我们报告了三个主要发现。第一，在精细尺度水平上，响应与协变量熵度量的多个有序显示结果表明，处于两个极端标签（高自尊和低自尊）的受试者表现出不同程度的不确定性。第二，在全局尺度水平上，在回答正面表述的问题时，自尊水平越高，不确定性程度越低；而在回答负面问题时，不确定性程度则会增加。第三，这种基于熵的计算模式在不同年龄组中都得以保留。我们提供了一组用R语言开发的工具，可随时用于分析评分数据以及在相关研究中探索基于模式的知识。
