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mirt: A Multidimensional Item Response Theory Package for the R Environment

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  • Chalmers, R. Philip

Abstract

Item response theory (IRT) is widely used in assessment and evaluation research to explain how participants respond to item level stimuli. Several R packages can be used to estimate the parameters in various IRT models, the most flexible being the ltm (Rizopoulos 2006), eRm (Mair and Hatzinger 2007), and MCMCpack (Martin, Quinn, and Park 2011) packages. However these packages have limitations in that ltm and eRm can only analyze unidimensional IRT models effectively and the exploratory multidimensional extensions available in MCMCpack requires prior understanding of Bayesian estimation convergence diagnostics and are computationally intensive. Most importantly, multidimensional confirmatory item factor analysis methods have not been implemented in any R package. The mirt package was created for estimating multidimensional item response theory parameters for exploratory and confirmatory models by using maximum-likelihood meth- ods. The Gauss-Hermite quadrature method used in traditional EM estimation (e.g., Bock and Aitkin'81) is presented for exploratory item response models as well as for confirmatory bifactor models (Gibbons and Hedeker'92). Exploratory and confirmatory models are estimated by a stochastic algorithm described by Cai (2010a,b). Various program comparisons are presented and future directions for the package are discussed.

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  • Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    • Handle: RePEc:jss:jstsof:v:048:i06
    DOI: http://hdl.handle.net/10.18637/jss.v048.i06
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    References listed on IDEAS

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    1. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    2. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
    3. Michael Edwards, 2010. "A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 474-497, September.
    4. Rizopoulos, Dimitris, 2006. "ltm: An R Package for Latent Variable Modeling and Item Response Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i05).
    5. Weeks, Jonathan P., 2010. "plink: An R Package for Linking Mixed-Format Tests Using IRT-Based Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i12).
    6. Sheng, Yanyan, 2010. "Bayesian Estimation of MIRT Models with General and Specific Latent Traits in MATLAB," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 34(i03).
    7. Martin, Andrew D. & Quinn, Kevin M. & Park, Jong Hee, 2011. "MCMCpack: Markov Chain Monte Carlo in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 42(i09).
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