关于含缺失数据的 Ising 网络分析的一则注记
A Note on Ising Network Analysis with Missing Data
AI总结：
针对缺失数据妨碍 Ising 模型伪似然推断、成列删除易致偏差的问题，提出结合迭代插补的条件贝叶斯框架，并辅以 Pólya-Gamma 增广与渐近理论，经模拟和 NESARC 数据验证有效。
摘要：
Ising 模型已成为分析项目反应数据的一种流行心理测量模型。由于标准似然方法在变量（即项目）众多时计算成本高昂，Ising 模型的统计推断通常通过伪似然进行。遗憾的是，缺失值的出现会阻碍伪似然的使用，而采用成列删除处理缺失数据的方法可能给估计带来显著偏差，有时还会产生误导性解释。本文提出了一个用于含缺失数据的 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。文中为该方法建立了渐近理论。此外，还提出了一种计算高效的 Pólya-Gamma 数据增广过程，以简化模型参数的抽样。该方法的性能通过模拟研究，以及对来自“全国酒精及相关疾病流行病学调查”（NESARC）的重性抑郁障碍和广泛性焦虑障碍数据的真实应用得到了展示。
英文摘要：
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{ó}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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
