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

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.

[1]  Jonathan P. Weeks.  plink: An R Package for Linking Mixed-Format Tests Using IRT-Based Methods , 2010 .

[2]  Dimitrios Rizopoulos.  ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses , 2006 .

[3]  Yanyan Sheng,et al.  Bayesian Estimation of MIRT Models with General and Specific Latent Traits in MATLAB , 2010 .

[4]  Eric T. Bradlow,et al.  Testlet Response Theory and Its Applications , 2007 .

[5]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[6]  Michael C. Edwards,et al.  A Markov Chain Monte Carlo Approach to Confirmatory Item Factor Analysis , 2010 .

[7]  Kevin Dowd,et al.  Monte Carlo Simulation Methods , 2013 .

[8]  Robert I. Jennrich,et al.  Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis , 2005 .

[9]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[10]  R. D. Bock,et al.  Marginal maximum likelihood estimation of item parameters , 1982 .

[11]  Mark D. Reckase,et al.  Item Response Theory: Parameter Estimation Techniques , 1998 .

[12]  Li Cai,et al.  HIGH-DIMENSIONAL EXPLORATORY ITEM FACTOR ANALYSIS BY A METROPOLIS–HASTINGS ROBBINS–MONRO ALGORITHM , 2010 .

[13]  Li Cai,et al.  Metropolis-Hastings Robbins-Monro Algorithm for Confirmatory Item Factor Analysis , 2010 .

[14]  Andrew D. Martin,et al.  MCMCpack: Markov chain Monte Carlo in R , 2011 .

[15]  G. Casella,et al.  Explaining the Gibbs Sampler , 1992 .

[16]  H. Robbins.  A Stochastic Approximation Method , 1951 .

[17]  R. P. McDonald,et al.  Test Theory: A Unified Treatment , 1999 .

[18]  P. Mair,et al.  Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R , 2007 .

[19]  R. D. Bock,et al.  Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm , 1981 .

[20]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[21]  Mark D. Reckase,et al.  The Discriminating Power of Items That Measure More Than One Dimension , 1991 .

[22]  James E. Carlson,et al.  Full-Information Factor Analysis for Polytomous Item Responses , 1995 .

[23]  Li Cai,et al.  A Two-Tier Full-Information Item Factor Analysis Model with Applications , 2010 .

[24]  R. D. Bock,et al.  High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature , 2005 .

[25]  R. Darrell Bock,et al.  Fitting a response model forn dichotomously scored items , 1970 .

[26]  Donald Hedeker,et al.  Full-information item bi-factor analysis , 1992 .

[27]  M. Reckase.  Multidimensional Item Response Theory , 2009 .

[28]  K. Holzinger,et al.  The Bi-factor method , 1937 .

[29]  F. Samejima.  Estimation of latent ability using a response pattern of graded scores , 1968 .

[30]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[31]  D. Thissen,et al.  Local Dependence Indexes for Item Pairs Using Item Response Theory , 1997 .

[32]  R. C. Durfee,et al.  MULTIPLE FACTOR ANALYSIS. , 1967 .

[33]  Melvin R. Novick,et al.  Some latent train models and their use in inferring an examinee's ability , 1966 .

[34]  E. Muraki,et al.  Full-Information Item Factor Analysis , 1988 .

[35]  R. Maruyama,et al.  On Test Scoring , 1927 .

[36]  Donald Hedeker,et al.  Full-Information Item Bifactor Analysis of Graded Response Data , 2007 .

[37]  Kristopher J Preacher,et al.  Item factor analysis: current approaches and future directions. , 2007, Psychological methods.

[38]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .