Alternative estimation approaches for some common Item Response Theory models
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In this report we give a brief introduction to Item Response Theory models and multilevel models. The general assumptions of two classical Item Response Theory, 1PL and 2PL models are discussed. We follow the discussion by introducing a multilevel level framework for these two Item Response Theory Models. We explain Bock and Aitkin's (1981) work to estimate item parameters for these two models. Finally we illustrate these models with a LSAT exam data and two statistical softwares; R project and Stata.
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