Theoretical Framework for Bayesian Hierarchical 2PLM with ADVI

My latest article from Cogn-IQ.org examines the Two-Parameter Logistic (2PL) Item Response Theory (IRT) model through a Bayesian hierarchical lens. This advanced approach introduces hierarchical priors on both respondent abilities and item parameters, allowing for more nuanced modeling of latent traits. The model also adopts Automatic Differentiation Variational Inference (ADVI), offering a scalable solution for handling large datasets, improving on traditional methods like Markov Chain Monte Carlo (MCMC). 

Key improvements introduced in the Bayesian hierarchical framework include better partial pooling of information, making it especially valuable in situations with sparse data. The article delves deep into the mathematical structure, outlining prior-likelihood functions and the importance of variational inference to ensure efficient posterior approximation. 

While the paper focuses on the theoretical aspects, future research could explore practical applications in fields like psychometrics, educational assessment, and machine learning. This method holds promise for more accurate latent trait estimation across various disciplines.

 

For more details, refer to the original article at https://www.cogn-iq.org/doi/09.2024/37693a22159f5fa4078d