Bayesian analysis of nonlinear structured latent factor models using a Gaussian Process Prior

TL;DR

This paper introduces a Bayesian nonlinear latent factor model with Gaussian process priors, improving flexibility in capturing complex relationships between observed variables and latent traits, with proven theoretical properties and practical validation.

Contribution

It proposes a novel Bayesian nonlinear factor analysis model with Gaussian process priors, ensuring identifiability and consistency, and demonstrates its effectiveness through simulations and real data.

Findings

Model effectively captures nonlinear relationships

Successfully identifies latent factors in simulations

Uncovers nonlinear patterns in real oil flow data

Abstract

Factor analysis models are widely utilized in social and behavioral sciences, such as psychology, education, and marketing, to measure unobservable latent traits. In this article, we introduce a nonlinear structured latent factor analysis model which is more flexible to characterize the relationship between manifest variables and latent factors. The confirmatory identifiability of the latent factor is discussed, ensuring the substantive interpretation of the latent factors. A Bayesian approach with a Gaussian process prior is proposed to estimate the unknown nonlinear function and the unknown parameters. Asymptotic results are established, including structural identifiability of the latent factors, consistency of the estimates of the unknown parameters and the unknown nonlinear function. Simulation studies and a real data analysis are conducted to investigate the performance of the proposed method. Simulation studies show our proposed method performs well in handling nonlinear model and successfully identifies the latent factors. Our analysis incorporates oil flow data, allowing us to uncover the underlying structure of latent nonlinear patterns.