PARTIALLY OBSERVED MIXTURES OF IRT MODELS: AN EXTENSION OF THE GENERALIZED PARTIAL CREDIT MODEL

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—on the one hand and the 2-parameter logistic (2PL) model on the other hand. The extension proposed here enables the use of the GPCM in discrete mixture item response theory (IRT) models with partially observed mixture information. Partially observed mixtures are discrete mixture distributions with missing grouping information for some, but not all, observations. This concept of partially observed mixtures integrates multigroup and mixture distribution IRT models. The proposed model includes the latent class analysis (LCA) and (multigroup) IRT models as well as mixture distribution IRT models as submodels. An application of the proposed partially observed mixture IRT model is presented. This application classifies about 80% of data from a large-scale mathematics assessment into three school types and estimates a mixture IRT model for the whole sample in which the grouping information is unknown for 20% of the sample. The aim of the method is twofold: first, to estimate the latent distributions by school type and, second, to unmix the data with missing school types into the groups established by the portion of the sample with known school-type information.

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