Ordinal Conditional Entropy Displays Reveal Intrinsic Characteristics of the Rosenberg Self-Esteem Scale.

Area of Science:

• Psychometrics
• Information Theory
• Data Analysis

Background:

• Ordinal and categorical rating data are often analyzed using methods for numerical data, despite inherent differences.
• Existing methods may not fully capture the nuances of uncertainty in subjective self-ratings.

Purpose of the Study:

• To explore the utility of conditional entropy for quantifying uncertainty in ordinal self-rating responses.
• To visualize and recognize patterns in response uncertainty using an ordinal axis display.
• To apply this methodology to the Rosenberg Self-Esteem Scale dataset.

Main Methods:

• Employed conditional entropy to measure uncertainty in responses to self-rating questions.
• Developed an ordinal display for visualizing entropy patterns against covariates.
• Analyzed an online dataset of responses to the Rosenberg Self-Esteem Scale.

Main Results:

• Fine-scale analysis revealed distinct uncertainty levels for subjects with high and low self-esteem.
• Global analysis showed decreasing uncertainty with higher self-esteem for positive items and increasing uncertainty for negative items.
• Observed that these entropy-based patterns remained consistent across different age groups.

Conclusions:

• Conditional entropy offers a novel approach to analyzing uncertainty in ordinal rating data.
• The findings highlight specific patterns of uncertainty related to self-esteem levels and question framing.
• The developed R tools facilitate the application of entropy-based analysis for pattern discovery in rating data research.