Generalized latent factor analysis not only provides a useful latent embedding approach in statistics and machine learning, but also serves as a widely used tool across various scientific fields, such as psychometrics, econometrics, and social sciences. Ensuring the identifiability of latent factors and the loading matrix is essential for the model's estimability and interpretability, and various identifiability conditions have been employed by practitioners. However, fundamental statistical inference issues for latent factors and factor loadings under commonly used identifiability conditions remain largely unaddressed, especially for correlated factors and/or non-orthogonal loading matrix. In this work, we focus on the maximum likelihood estimation for generalized factor models and establish statistical inference properties under popularly used identifiability conditions. The developed theory is further illustrated through numerical simulations and an application to a personality assessment dataset.

翻译：广义潜因子分析不仅为统计学和机器学习提供了有效的潜在嵌入方法，还在心理测量学、计量经济学和社会科学等多个科学领域得到广泛应用。确保潜因子和载荷矩阵的可识别性对于模型的可估计性和可解释性至关重要，研究者们已采用了多种可识别性条件。然而，在常用可识别性条件下，潜因子和因子载荷的基础统计推断问题仍未得到充分解决，特别是对于相关因子和/或非正交载荷矩阵的情况。本研究聚焦于广义因子模型的极大似然估计，在广泛采用的可识别性条件下建立了统计推断性质。通过数值模拟和人格评估数据集的实证应用，进一步验证了所发展理论的有效性。