Questionnaire data analysis using information geometry.

Area of Science:

• Statistics
• Data Science
• Statistical Physics

Background:

• Questionnaire data analysis often requires reducing high-dimensional responses to a lower dimension.
• Common methods like PCA, MCA, or t-SNE struggle with categorical variables and unmet statistical assumptions.
• Statistical manifolds (SM) offer a theoretical framework connecting statistical models and physical phenomena.

Purpose of the Study:

• To develop a non-parametric dimensionality reduction technique for questionnaire data, particularly effective for categorical variables.
• To create a low-dimensional embedding of the statistical manifold representing questionnaire responses.
• To demonstrate the method's utility on both simulated and real-world categorical datasets.

Main Methods:

• A novel non-parametric approach based on Fisher Information was developed.
• The method generates a low-dimensional embedding of a statistical manifold (SM).
• Simulations and two empirical datasets (anthropological survey, health inequality cohort) were used for validation.

Main Results:

• The Fisher Information-based method successfully created low-dimensional embeddings for complex questionnaire data.
• It demonstrated superior performance in discriminating between different behaviors compared to existing methods.
• The approach proved effective even with predominantly categorical variables.

Conclusions:

• The proposed non-parametric method offers a powerful tool for analyzing high-dimensional questionnaire data with categorical variables.
• It provides effective dimension reduction comparable to methods used for continuous data.
• This approach enhances the discrimination of behavioral patterns in complex datasets.