The generalized partial-credit model (GPCM) is used frequently in educational testing and in large-scale assessments for analyzing polytomous data. Special cases of the generalized partial-credit model are the partial-credit model—or Rasch model for ordinal data—and the two-parameter logistic (2PL) model. This article extends the GPCM to the class of discrete mixture distribution models. The developments presented here extend models such as the mixed Rasch model and dichotomous multiparameter item response theory (IRT) mixture models. In addition, the model proposed here allows estimation of multigroup models with partially missing grouping information. An application of the proposed partially observed mixture IRT model to a sparse matrix sample of item responses from a national large-scale assessment program is also presented.
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