Identifiability and Inference for Generalized Latent Factor Models

TL;DR

This paper develops statistical inference methods for generalized latent factor models, addressing identifiability issues and providing theoretical guarantees for maximum likelihood estimation in complex settings.

Contribution

It introduces a comprehensive inference framework for generalized factor models under common identifiability conditions, including correlated factors and non-orthogonal loadings.

Findings

Theoretical properties of MLE established under various conditions.

Numerical simulations validate the inference methods.

Application to personality data demonstrates practical utility.

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.