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. 2015 Aug;75(4):585-609.
doi: 10.1177/0013164414551411. Epub 2014 Sep 25.

Using SAS PROC MCMC for Item Response Theory Models

Allison J Ames  1 , Kelli Samonte  1
Affiliations

Using SAS PROC MCMC for Item Response Theory Models

Allison J Ames et al. Educ Psychol Meas. 2015 Aug.

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.

Keywords: Markov chain Monte Carlo; item response theory; software.

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Conflict of interest statement

Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1.
Figure 1.
Estimated parameter comparisons.
Figure 2.
Figure 2.
Illustration of the random walk Metropolis–Hasting algorithm.
Listing 1.
Listing 1.
One-Parameter Logistic Item Response Theory Model.
Figure 3.
Figure 3.
Diagnostic plots.
Listing 2.
Listing 2.
Two-Parameter Logistic Item Response Theory Model.
Listing 3.
Listing 3.
Three-Parameter Logistic Item Response Theory Model.
Listing 4.
Listing 4.
Generalized Partial Credit Item Response Theory Model, Replicating Li and Baser (2012).
Listing 5.
Listing 5.
Graded Response Item Response Theory Model.
Listing 6.
Listing 6.
MIRT Model.
Figure 4.
Figure 4.
Multidimensional item response theory model parameter recovery.
See this image and copyright information in PMC

References

    1. Andrews M., Baguley T. (2013). Prior approval: The growth of Bayesian methods in psychology. British Journal of Mathematical and Statistical Psychology, 66, 1-7. - PubMed
    1. Andrich D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573.
    1. *Baldwin P., Bernstein J., Wainer H. (2009). Hip psychometrics. Statistics in Medicine, 28, 2277-2292. - PubMed
    1. Bock R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
    1. *Bolfarine H., Bazan J. (2010). Bayesian estimation of the logistic positive exponent IRT model. Journal of Educational and Behavioral Statistics, 35, 693-713.

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