School of Statistics, East China Normal University, Columbia House, Room 5.16 Houghton Street, WC2A 2AE, London, UK.
Department of Statistics, London School of Economics and Political Science, Room 5.16 Columbia House, Houghton Street, London, WC2A 2AE, UK.
Psychometrika. 2024 Dec;89(4):1186-1202. doi: 10.1007/s11336-024-09985-2. Epub 2024 Jul 6.
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 Pólya-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).
Ising 模型已成为分析项目反应数据的一种流行心理计量学模型。Ising 模型的统计推断通常通过拟似然进行,因为当变量(即项目)较多时,标准似然方法的计算成本很高。不幸的是,缺失值的存在会阻碍拟似然的使用,而对于缺失数据的处理,采用完全删除的方法可能会给估计带来很大的偏差,有时会产生误导性的解释。本文提出了一种带有缺失数据的 Ising 网络分析的条件贝叶斯框架,该框架将拟似然方法与迭代数据插补相结合。为该方法建立了渐近理论。此外,还提出了一种计算效率高的 Pólya-Gamma 数据扩充程序,以简化模型参数的抽样。该方法的性能通过模拟和对来自国家酒精和相关条件流行病学调查(NESARC)的重度抑郁和广泛性焦虑障碍数据的实际应用进行了展示。