There has been regained interest in joint maximum likelihood (JML) estimation of item factor analysis (IFA) recently, primarily due to its efficiency in handling high-dimensional data and numerous latent factors. It has been established under mild assumptions that the JML estimator is consistent as both the numbers of respondents and items tend to infinity. The current work presents an efficient Riemannian optimization algorithm for JML estimation of exploratory IFA with dichotomous response data, which takes advantage of the differential geometry of the fixed-rank matrix manifold. The proposed algorithm takes substantially less time to converge than a benchmark method that alternates between gradient ascent steps for person and item parameters. The performance of the proposed algorithm in the recovery of latent dimensionality, response probabilities, item parameters, and factor scores is evaluated via simulations.

中文翻译：

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高维探索性项目因子分析联合最大似然估计的黎曼优化算法

最近，项目因子分析 (IFA) 的联合最大似然 (JML) 估计重新引起了人们的兴趣，这主要是由于它在处理高维数据和众多潜在因素方面的效率。已经在温和的假设下建立了 JML 估计量是一致的，因为受访者和项目的数量都趋于无穷大。当前的工作提出了一种有效的黎曼优化算法，用于具有二分响应数据的探索性 IFA 的 JML 估计，该算法利用了固定秩矩阵流形的微分几何。与在人员和项目参数的梯度上升步骤之间交替的基准方法相比，所提出的算法收敛所需的时间要少得多。所提出的算法在潜在维数恢复方面的性能，