Estimating Discrete Latent Variable Models Using Amortized Variational Inference

Area of Science:

• Computational Statistics
• Psychometrics
• Machine Learning

Background:

• Amortized variational inference (AVI) shows promise for efficient estimation of high-dimensional latent variable models.
• Current applications of AVI are largely confined to item response theory (IRT), with limited generalization to discrete latent variable models.
• Estimating complex, high-dimensional models often presents computational challenges for traditional methods.

Purpose of the Study:

• To generalize amortized variational inference (AVI) for estimating discrete latent variable models.
• To evaluate the computational efficiency and accuracy of AVI compared to marginal maximum likelihood (MML) and standard variational inference (VI).
• To demonstrate the practical application of AVI in high-dimensional mixture IRT models.

Main Methods:

• Proposed two novel approaches to adapt AVI for discrete latent variable models.
• Validated methods using simulations for latent class analysis and generalized deterministic inputs, noisy and gate (GDI-NG) models.
• Applied AVI to estimate a seven-dimensional mixture IRT model for a narcissism inventory, including computation of bootstrapped standard errors.

Main Results:

• Simulations confirmed AVI's ability to accurately estimate simple discrete latent variable models.
• AVI demonstrated computational advantages over MML and standard VI for mixture IRT models.
• The proposed AVI approach successfully estimated a high-dimensional mixture IRT model, outperforming quadrature-based methods and enabling standard error computation.

Conclusions:

• The developed AVI methods effectively extend its application to discrete latent variable models, including mixture IRT.
• AVI offers a computationally efficient alternative for estimating complex, high-dimensional latent variable models.
• The study provides accessible code and tools for implementing AVI in latent variable modeling.