A Note on Ising Network Analysis with Missing Data

TL;DR

This paper introduces a Bayesian method for Ising network analysis that effectively handles missing data through iterative imputation and a Pólya-Gamma augmentation, improving inference accuracy and computational efficiency.

Contribution

It proposes a novel conditional Bayesian framework combining pseudo-likelihood with data imputation for Ising models with missing data, supported by asymptotic theory and efficient sampling techniques.

Findings

Method performs well in simulations.

Applied successfully to mental health survey data.

Reduces bias caused by missing data in network analysis.

Abstract

The Ising model has become a popular psychometric model for analyzing item response data. The statistical inference of the Ising model is typically carried out via a pseudo-likelihood, as the standard likelihood approach suffers from a high computational cost when there are many variables (i.e., items). Unfortunately, the presence of missing values can hinder the use of pseudo-likelihood, and a listwise deletion approach for missing data treatment may introduce a substantial bias into the estimation and sometimes yield misleading interpretations. This paper proposes a conditional Bayesian framework for Ising network analysis with missing data, which integrates a pseudo-likelihood approach with iterative data imputation. An asymptotic theory is established for the method. Furthermore, a computationally efficient {P{\'o}lya}-Gamma data augmentation procedure is proposed to streamline the sampling of model parameters. The method's performance is shown through simulations and a real-world application to data on major depressive and generalized anxiety disorders from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC).