Modeling Nonlinear Relationships in Psychometric Data Using Variational Autoencoders: Insights from Simulated Data

Psychometric research relies on latent variables analysis, employing techniques like factor analysis to explore test structures. However, such methods often assume linear dimensionality reduction, not always reflective of psychological data complexities. This paper introduces Artificial Neural Networks (ANNs) as a solution, promising nonlinear exploration of latent space. We implement a Variational Autoencoder (VAE), an ANN which can perform nonlinear dimensionality reduction and distribution learning. We evaluate VAE's performance using two simulated datasets. Results show that VAE are comparable to Factor Analysis in linear scenarios, accurately reproducing factor scores. However, in nonlinear scenarios, VAE outperforms Factor Analysis by capturing nonlinear relationships and enhancing factor score estimations. This research underscores VAE's utility in advancing latent variable exploration beyond traditional linear methods.