ESTIMATING HETEROGENEOUS GRAPHICAL MODELS FOR DISCRETE DATA WITH AN APPLICATION TO ROLL CALL VOTING.

Area of Science:

• Statistics
• Network Analysis
• Computational Social Science

Background:

• Analyzing discrete data across multiple categories often reveals shared underlying structures.
• Understanding heterogeneous dependence structures is crucial for complex systems like legislative voting.

Purpose of the Study:

• To develop a novel Markov graphical model for jointly estimating collections of graphical models with shared structure.
• To propose a joint estimation method that preserves commonalities while allowing for network differences.
• To apply the method to U.S. Senate voting data to uncover issue-specific and overarching bipartisan structures.

Main Methods:

• Development of a Markov graphical model tailored for discrete data with shared network structures.
• Implementation of a joint estimation technique utilizing a group penalty to identify common zero interaction effects across networks.
• Application and validation of the method on simulated data and U.S. Senate voting records.

Main Results:

• The proposed method successfully extracts both issue-specific network structures and a common bipartisan structure from U.S. Senate voting data.
• The analysis demonstrates that individual issue networks are distinct yet share an underlying common structure.
• Consistency of the method for parameter estimation and model selection was theoretically established.

Conclusions:

• The developed method effectively models and estimates heterogeneous dependence structures in collections of graphical models.
• It provides a powerful tool for uncovering both shared and distinct network properties in multi-category data.
• The findings offer insights into the complex network structures within legislative bodies.