A Comparison of Two Markov Chain Monte Carlo Algorithms for the Three-Parameter Logistic (3PL) Item Response Theory Model

• In Event: Modern Applications in Item Response Theory

Abstract

The fully Bayesian estimation using Markov chain Monte Carlo (MCMC) techniques has become popular for estimating item response theory (IRT) models. The current development of MCMC includes two popular algorithms: Gibbs sampling and No-U-Turn sampler (NUTS). While the former has been used with fitting various IRT models, the latter is relatively new, requiring research to compare it with other algorithms. The purpose of the present study is to evaluate the performances of these two MCMC algorithms in estimating the three-parameter logistic (3PL) IRT model. The results suggest that NUTS performs better than Gibbs sampling under most of the test conditions. Findings also shed light on the use of MCMC with more complex IRT models, especially those with a lower-asymptote.

Authors

• Meng-I Chang, Southern Illinois University - Carbondale

• Yanyan Sheng, Southern Illinois University - Carbondale