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).

翻译：Ising模型已成为分析项目响应数据的流行心理测量模型。由于标准似然方法在变量（即项目）较多时计算成本高昂，Ising模型的统计推断通常通过伪似然方法进行。然而，缺失值的存在会阻碍伪似然方法的使用，而针对缺失数据的列表删除处理方法可能在估计中引入显著偏差，有时甚至导致误导性解释。本文提出了一种适用于含缺失数据的Ising网络分析的条件贝叶斯框架，该框架将伪似然方法与迭代数据插补相结合。同时建立了该方法的渐近理论。此外，为简化模型参数的采样过程，提出了计算高效的Pólya-Gamma数据增广算法。通过模拟实验以及基于国家酒精及相关疾病流行病学调查(NESARC)中重性抑郁障碍和广泛性焦虑障碍数据的实际应用，展示了该方法的性能。