Using SAS PROC MCMC for Item Response Theory Models

Abstract

Interest in using Bayesian methods for estimating item response theory models has grown at a remarkable rate in recent years. This attentiveness to Bayesian estimation has also inspired a growth in available software such as WinBUGS, R packages, BMIRT, MPLUS, and SAS PROC MCMC. This article intends to provide an accessible overview of Bayesian methods in the context of item response theory to serve as a useful guide for practitioners in estimating and interpreting item response theory (IRT) models. Included is a description of the estimation procedure used by SAS PROC MCMC. Syntax is provided for estimation of both dichotomous and polytomous IRT models, as well as a discussion on how to extend the syntax to accommodate more complex IRT models.

Using the Stan Program for Bayesian Item Response Theory

“…In addition, it allows interface with other software programs such as R, Python, Matlab, Stata, Julia, as well as its compatibility with all three major operating platforms, namely Linux, Mac, and Windows. Curtis (2010) introduced WinBUGS codes for several IRT models while other researchers (Ames & Samonte, 2015;Stone & Zhu, 2015) presented on using SAS PROC MCMC for IRT model parameter estimation. Despite its efficiency and easy accessibility in different interfaces, no article collectively introduces Stan codes for IRT model parameter estimation.…”

Subjective Priors for Item Response Models: Application of Elicitation by Design

“…Samples of n = 40 and n = 100 examinees were randomly drawn from a larger administration of the ERIT ( n = 412) given in February 2016 to university sophomores. Estimation was performed in SAS using the MCMC procedure that relies upon the Metropolis‐Hastings sampler (see Ames & Samonte, ; Stone & Zhu, , for more details). Convergence was assessed visually via trace plots, and using formal approaches such as Geweke's () diagnostic.…”

“…There has been continual growth in the number of researchers using Bayesian methods in empirical research and applications in educational measurement, research, and evaluation (Ames & Samonte, ; Andrews & Baguley, ; Levy, ; Wainer, ). This advance is attributed to the well‐documented benefits of Bayesian inference (see, for example, Mislevy, ; Swaminathan & Gifford, , , ), as well as advances in computing power and accessibility of software programs.…”

A Review of PROC IRT in SAS

“…PROC GLIMMIX estimates the model parameters through a pseudo-likelihood approach: Instead of direct maximization of the A Review of PROC IRT in SAS approximated full likelihood, PROC GLIMMIX iteratively derives and fits generalized estimating equations until convergence (SAS Institute, 2015). PROC MCMC can be used to fit a wide variety of IRT models and extensions (Ames & Samonte, 2014;Stone & Zhu, 2015) with the Bayesian method for person and item parameter estimation. PROC MCMC implements the Markov chain Monte Carlo method with the random walk Metropolis-Hastings algorithm.…”