Thesis Presentation: Alex Nguyen
Title: Marginal Likelihood Estimation in Item Response Theory Models
Abstract: This dissertation investigates the use of Marginal likelihood estimation for Bayesian model comparison in Item Response Theory (IRT), focusing on 2-Parameter Logistic (2PL) models and their finite mixture extensions. Bayesian model comparison uses the Bayes factor, which is defined as the ratio of the marginal likelihood of the competing models. These are typically estimated via Monte Carlo methods, with bridge sampling being a popular and general purpose approach. However, it can become in-efficient when models are high dimensional.
The study applies bridge sampling to both standard 2PL models and finite mixture 2PL models, which allow the latent ability distribution to follow a flexible mixture of Gaussians. To improve estimation, we introduce a marginalization strategy that integrates out the latent abilities using a grid-based approximation. This approach avoids direct sampling of discrete cluster assignments and reduces the dimensionality of the posterior samples, resulting in faster and more stable computation.
Using simulated data under unimodal, bimodal, and multimodal ability distributions, we evaluate the effectiveness of bridge sampling in recovering calibrated Bayes factors. Results show that while finite mixture models are more flexible, the standard 2PL model can outperform them in cases where the true ability distribution is unimodal. This work provides practical insights into the application of bridge sampling for psychometric data analysis and demonstrates its potential to enhance Bayesian model evaluation in high-dimensional settings.
Advisor: Sally Paganin
