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Maximum Marginal Likelihood Estimation With an Expectation - Maximization Algorithm for Multigroup/Mixture Multidimensional Item Response Theory Models IRT MIRT GPCM GRM 3PL

Fu, Jianbin
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Item Response Theory (IRT), Multidimensional Item Response Theory (MIRT), Marginal Maximum Likelihood Estimation, Item Parameters, Generalized Partial-Credit Model (GPCM), Graded Response Models (GRM), 3-Parameter Logistic Model (3PL)


A maximum marginal likelihood estimation with an expectation–maximization algorithm has been developed for estimating multigroup or mixture multidimensional item response theory models using the generalized partial credit function, graded response function, and 3‐parameter logistic function. The procedure includes the estimation of item parameters, attribute population distribution parameters, and test takers' attributes. All estimation functions and derivatives are provided. This procedure has been implemented in an R program. A simulation study has been conducted using this R program on various models related to the generalized partial credit function, and the result shows reasonable parameter recovery.

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