Exploring dependence between categorical variables: Benefits and limitations of using variable selection within...

Area of Science:

• Statistics
• Data Analysis
• Machine Learning

Background:

• Categorical variables present complex dependence structures.
• Log-linear models and Bayesian clustering are used to explore these structures.
• Integrating these methods can improve data analysis.

Purpose of the Study:

• To relate Bayesian partitioning of covariate space with log-linear modeling.
• To explore how clustering can aid log-linear model determination.
• To demonstrate the advantages and limitations of this integrated approach.

Main Methods:

• Deriving theoretical results connecting Bayesian partitioning and log-linear models.
• Incorporating variable selection within Bayesian clustering.
• Applying methods to simulated and real-world sparse contingency tables.

Main Results:

• Bayesian clustering, with variable selection, can reduce covariates and simplify log-linear model exploration.
• This approach is particularly advantageous for sparse contingency tables.
• Clustering structure does not consistently inform about the existence of interactions.

Conclusions:

• Integrating Bayesian clustering with variable selection can enhance log-linear model determination, especially for high-dimensional sparse data.
• The method aids in identifying key covariates and reducing model complexity.
• Limitations exist in consistently identifying interaction effects through clustering alone.