Identifiability and Inference for Generalized Latent Factor Models

2025-08-07

AI Summary

In generalized latent factor models, existing identifiability conditions fail to support valid statistical inference for latent factors and loadings when factors are correlated and the loading matrix is non-orthogonal. Method: We develop a rigorous maximum likelihood estimation framework compatible with standard identifiability constraints—such as standardization of the factor covariance matrix or lower-triangularization of the loading matrix. Contribution/Results: This work provides the first systematic asymptotic inference theory for correlated factors and non-orthogonal loadings, establishing consistency, asymptotic normality, and explicit covariance structures for both factor score estimators and loading parameters. Through theoretical analysis, Monte Carlo simulations, and empirical application to real personality assessment data, we demonstrate the method’s validity, robustness, and practical utility. Our approach substantially enhances interpretability and broadens the applicability of latent factor models in psychometrics and related fields.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Addresses identifiability issues in generalized latent factor models
• Establishes statistical inference for correlated latent factors
• Develops theory for non-orthogonal loading matrix estimation

Innovation

• Maximum likelihood estimation for generalized factor models
• Statistical inference under identifiability conditions
• Theory validation through simulations and applications