Generative Adversarial Networks for High-Dimensional Item Factor Analysis: A Deep Adversarial Learning Algorithm.

Area of Science:

• Psychometrics
• Machine Learning
• Statistical Modeling

Background:

• Deep learning advances have improved item factor analysis (IFA) within item response theory (IRT).
• Variational autoencoders (VAEs) are common for high-dimensional latent variables in IFA, but their inference networks have limitations.
• Limited expressiveness in VAE inference networks can impede performance in IFA.

Purpose of the Study:

• Introduce Adversarial Variational Bayes (AVB) and importance-weighted AVB (IWAVB) as advanced inference algorithms for IFA.
• Enhance the flexibility and performance of latent variable modeling in IFA.
• Enable scaling IFA to complex, large-scale, and multimodal datasets.

Main Methods:

• Combined VAEs with generative adversarial networks (GANs) to create AVB.
• Utilized an auxiliary discriminator network in AVB to frame estimation as a two-player game.
• Developed an importance-weighted extension (IWAVB) for enhanced flexibility and likelihood estimation.

Main Results:

• AVB and IWAVB theoretically achieve likelihoods matching or exceeding VAEs and importance-weighted autoencoders (IWAEs).
• Empirical data analysis showed IWAVB achieved higher likelihoods than IWAE, indicating greater expressiveness.
• Simulations demonstrated IWAVB's comparable parameter recovery and superior performance with multimodal latent distributions compared to IWAE.

Conclusions:

• IWAVB offers a more expressive and flexible inference approach for item factor analysis.
• The proposed methods facilitate the integration of psychometrics with modern multimodal data analysis.
• IWAVB shows promise for applying IFA to complex, large-scale, and multimodal data settings.