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

R. Philip Chalmers

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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 1981) is presented for exploratory item response models as well as for confirmatory bifactor models (Gibbons and Hedeker 1992). 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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