# Bayes Factor Tests for Group Differences in Ordinal and Binary Graphical Models

## TL;DR

This paper introduces Bayes factor tests to compare network structures between groups using binary or ordinal data, with an implementation in an R package.

## Contribution

The paper introduces Bayes factor tests for assessing group differences in networks of binary or ordinal variables.

## Key findings

- The proposed Bayes factor tests are implemented in the R package bgms.
- Numerical illustrations demonstrate the correctness and performance of the methods in realistic scenarios.

## Abstract

Multivariate analysis of psychological variables using graphical models has become a standard analysis in the psychometric literature. Most cross-sectional measures are either binary or ordinal, and the methodology for inferring the structure of networks of binary and ordinal variables is developing rapidly. In practice, however, research questions often focus on whether and how networks differ between observed groups. While Bayes factor methods for inferring network structure are well established, a similar methodology for assessing group differences in networks of binary or ordinal variables is currently lacking. In this article, we extend the Bayesian framework for the analysis of ordinal Markov random fields, a network model for binary and ordinal variables, and develop Bayes factor tests for assessing parameter differences in the networks of two independent groups. The proposed methods are implemented in the R package bgms, and we use numerical illustrations to show that the implemented methods work correctly and how well the methods work compared to existing methods in situations resembling empirical research.