Identifiability and Inference for Generalized Latent Factor Models

• 成果类型: Article; Early Access
• 署名作者: Cui, Chengyu; Xu, Gongjun
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2687835
• 发表日期: 2026-07-23
• 关键词: identifiability; Nonlinear latent factor model; Statistical inference; principal components; analytic rotation; uniqueness; number

摘要

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 latent 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.