A Short Note on Obtaining Item Parameter Estimates of IRT Models with Bayesian Estimation in Mplus

Sedat Şen,Seock-Ho Kim,Allan Cohen

doi:10.21031/epod.693719

Sedat Şen, Seock-Ho Kim + Show 1 more

Open Access

https://doi.org/10.21031/epod.693719

Copy DOI

Abstract

Parameter estimation of Item Response Theory (IRT) models can be applied using both Bayesian and non-Bayesian methods. Although maximum likelihood estimation (MLE), a non-Bayesian method, has predominated since the 1970s, there is an increasing use of Bayesian methods, due to their capability for estimating complex models and for their implementation in commercially available software. In view of the recent increase in the popularity of these methods, a comparison between model parameter estimates from the two types of methods would be useful for practitioners. In this study, we compare MLE and Bayesian estimation, two popular methods for obtaining parameter estimates for dichotomous IRT models, using the MLE and Bayes estimator options as implemented in the Mplus software package. Results indicated Bayesian and MLE estimates differed only slightly, clearly demonstrating the consistency between estimates from the two methods. Further, Bayes estimator option in Mplus can be a viable and relatively easy to use tool for calibrations of IRT models.

Highlights

Item response theory (IRT) models have been used for testing over the last half-century
Bayesian estimation of IRT models is sometimes preferable to maximum likelihood estimation (MLE) as MLE needs numerical integration, which can be slow or prohibitive depending on the numbers of dimensions of integration as a function of the numbers of latent variables
We provide a simplified step-by-step method for the estimation of dichotomous IRT models with Bayesian estimation

Summary

Introduction

Item response theory (IRT) models have been used for testing over the last half-century (van der Linden & Hambleton, 2013). Parameter estimation is considered one of the important processes of IRT modeling. Estimates of IRT model parameters have typically been done using methods such as maximum likelihood estimation (MLE; Bock & Aitkin, 1981) and Markov chain Monte Carlo estimation (MCMC; Patz & Junker, 1999a). MLE methods are based on a frequentist approach, and MCMC is a Bayesian method. MLE-based estimation methods have been widely used in IRT modeling since the development of software such as BILOG (Zimowski, Muraki, Mislevy, & Bock, 2003), MULTILOG (Thissen, 1991) and PARSCALE (Muraki & Bock, 1996). Implementations of MCMC methods for estimation of IRT models began to be reported in the early 1990s (e.g., Albert, 1992; Albert & Chib, 1993). MLE generally requires large samples to produce reliable results (e.g., Asparouhov & Muthén, 2010a; Meuleman & Billiet, 2009), a condition not necessarily required by Bayesian methods

Objectives

Methods

Results

Conclusion