Parameter Recovery with Marginal Maximum Likelihood and Markov Chain Monte Carlo Estimation for the Generalized Partial Credit Model

TL;DR

This study compares the effectiveness of marginal maximum likelihood and Markov chain Monte Carlo methods in recovering parameters of the generalized partial credit model, revealing conditions where each method performs better.

Contribution

It provides the first comprehensive comparison of MMLE and MCMC for GPCM parameter recovery through extensive simulation and real data analysis.

Findings

MCMC has less bias for item discrimination under normal and uniform distributions.

MMLE outperforms MCMC in skewed latent distributions.

No significant difference in item location and ability parameter recovery.

Abstract

The generalized partial credit model (GPCM) is a popular polytomous IRT model that has been widely used in large-scale educational surveys and health care services. Same as other IRT models, GPCM can be estimated via marginal maximum likelihood estimation (MMLE) and Markov chain Monte Carlo (MCMC) methods. While studies comparing MMLE and MCMC as estimation methods for other polytomous IRT models such as the nominal response model and the graded response model exist in literature, no studies have compared how well MMLE and MCMC recover the model parameters of GPCM. In the current study, a comprehensive simulation study was conducted to compare parameter recovery of GPCM via MMLE and MCMC. The manipulated factors included latent distribution, sample size, and test length, and parameter recovery was evaluated with bias and root mean square error. It was found that there were no statistically significant differences in recovery of the item location and ability parameters between MMLE and MCMC; for the item discrimination parameter, MCMC had less bias in parameter recovery than MMLE under both normal and uniform latent distributions, and MMLE outperformed MCMC with less bias in parameter recovery under skewed latent distributions. A real dataset from a high-stakes test was used to demonstrate the estimation of GPCM with MMLE and MCMC. Keywords: polytomous IRT, GPCM, MCMC, MMLE, parameter recovery.