Autoencoders for Amortized Joint Maximum Likelihood Estimation of Confirmatory Item Factor Models

Area of Science:

• Statistics
• Machine Learning
• Psychometrics

Background:

• Item factor models are crucial for analyzing complex data structures.
• Traditional estimation methods for high-dimensional factor models can be computationally intensive and require parameter constraints.
• Neural networks, specifically variational autoencoders, offer a promising alternative for statistical modeling.

Purpose of the Study:

• To demonstrate the advantages of a specific autoencoder for amortized joint maximum likelihood estimation of item factor models.
• To compare the performance of the autoencoder against constrained joint maximum likelihood and marginal maximum likelihood estimation methods.
• To highlight the efficiency and reduced bias offered by the autoencoder approach.

Main Methods:

• Utilized a specific variational autoencoder architecture for amortized joint maximum likelihood estimation.
• Conducted a simulation study comparing the autoencoder with constrained joint maximum likelihood and marginal maximum likelihood.
• Evaluated performance under various factor score distributions and assessed bias in factor score estimates.

Main Results:

• The autoencoder approach for joint maximum likelihood estimation requires no additional parameter constraints for standard asymptotic theory.
• Amortized joint maximum likelihood estimates of factor scores derived from the autoencoder were found to be less biased overall.
• The autoencoder demonstrated efficient estimation for high-dimensional item factor models.

Conclusions:

• Variational autoencoders provide an efficient and effective tool for amortized joint maximum likelihood estimation in item factor models.
• The proposed autoencoder method overcomes limitations of conventional estimation techniques by avoiding parameter constraints and reducing bias.
• The study illustrates the practical applicability of autoencoders in statistical analysis through real data examples.