In this paper, we explore the use of the stochastic EM algorithm (Celeux & Diebolt (1985) Computational Statistics Quarterly, 2, 73) for large‐scale full‐information item factor analysis. Innovations have been made on its implementation, including an adaptive‐rejection‐based Gibbs sampler for the stochastic E step, a proximal gradient descent algorithm for the optimization in the M step, and diagnostic procedures for determining the burn‐in size and the stopping of the algorithm. These developments are based on the theoretical results of Nielsen (2000, Bernoulli, 6, 457), as well as advanced sampling and optimization techniques. The proposed algorithm is computationally efficient and virtually tuning‐free, making it scalable to large‐scale data with many latent traits (e.g. more than five latent traits) and easy to use for practitioners. Standard errors of parameter estimation are also obtained based on the missing‐information identity (Louis, 1982, Journal of the Royal Statistical Society, Series B, 44, 226). The performance of the algorithm is evaluated through simulation studies and an application to the analysis of the IPIP‐NEO personality inventory. Extensions of the proposed algorithm to other latent variable models are discussed.

中文翻译：

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一种用于大规模全信息项因子分析的改进的随机EM算法。

在本文中，我们探索了使用随机EM算法（Celeux＆Diebolt（1985）计算统计季刊，第2卷，第73页）进行大规模的全面信息项因子分析。其实施方面已进行了一些创新，包括用于随机E步的基于自适应拒绝的Gibbs采样器，用于M步优化的近端梯度下降算法以及用于确定老化尺寸和停止M的诊断程序。算法。这些发展是基于Nielsen（2000，Bernoulli，6（457）以及先进的采样和优化技术。所提出的算法在计算上是有效的，并且几乎没有调优，使其可扩展到具有许多潜在特征（例如，超过五个潜在特征）的大规模数据，并且易于从业人员使用。（路易斯，1982年基础上，缺少信息的身份也获得了参数估计的标准误差皇家统计学会，B系列，44，226）。该算法的性能通过仿真研究以及在IPIP‐NEO人格清单分析中的应用进行评估。讨论了该算法对其他潜在变量模型的扩展。