Marginal Likelihood Estimation in Bayesian Item Response Theory Models

Music City Center 

Item Response Theory (IRT) models are widely used in psychometrics to measure latent traits like ability from test responses. Standard IRT models assume a fixed trait distribution, which may not capture population differences. To address this, Bayesian nonparametric (BNP) IRT models use priors such as the Chinese Restaurant Process (CRP) to allow data-driven clustering of individuals. While this increases flexibility, it also adds computational complexity, making accurate marginal likelihood estimation crucial for comparing BNP and parametric models using Bayes factors, especially in high-dimensional settings. Bridge sampling provides a more stable alternative to traditional Monte Carlo methods but must be adapted to handle the discrete clustering structure of BNP models.

This work develops a two-step method for marginal likelihood estimation in BNP IRT models. First, latent traits are integrated out using the model's structure, reducing computation. Second, bridge sampling is refined, incorporating moment-matching and variance reduction techniques to improve accuracy. Simulation results show that this method enhances efficiency and precision.

Bridge Sampling

Bayes Factor

Hierarchical Models

Latent Variables

Monte Carlo Methods

Nonparametric Clustering 

Section on Bayesian Statistical Science