Bayesian Inference for IRT Models with Non-Normal Latent Trait Distributions.

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Item response theory (IRT) models commonly assume normal latent traits.
• Violations of this normality assumption can impact parameter estimation accuracy.
• Flexible distributions are needed to model diverse psychological and educational constructs.

Purpose of the Study:

• To present a novel Markov chain Monte Carlo (MCMC) method for ordinal IRT models.
• To incorporate flexible latent trait distributions using Davidian curves (DCs).
• To evaluate the performance of the proposed MCMC algorithm against existing methods.

Main Methods:

• Developed a new MCMC algorithm utilizing Davidian curves (DCs) for flexible latent trait distributions.
• Conducted a simulation study manipulating the number of response categories, sample size, and latent trait distribution shape.
• Compared the MCMC-DC method with an existing Expectation-Maximization (EM) method using DCs.
• Employed the Hanna-Quinn (HQ) criterion for selecting the optimal DC order.

Main Results:

• The MCMC algorithm with DCs effectively fit flexible distributions when informative priors were used.
• The proposed method yielded good parameter estimates.
• Under certain conditions, the MCMC-DC method demonstrated lower bias and Root Mean Square Error (RMSE) compared to the EM-DC method.

Conclusions:

• The novel MCMC algorithm with Davidian curves offers a viable approach for IRT models with non-normal latent traits.
• This method provides accurate parameter estimates and can outperform traditional EM methods in specific scenarios.
• The use of flexible distributions enhances the robustness and applicability of IRT models.