Item response theory (IRT) models show the relationship between the ability or trait (θ) measured by the instrument and an item response. Both the IRT and classical test theory (CTT) indices and how they are related in terms of item parameters, conceptualization of reliability and standard error of measurement, and population invariance are described. The IRT indices are more readily understood in the context of the formal mathematical models for describing the item response probabilities, in which these models are discussed. The IRT indices are introduced only in general terms. The three-parameter logistic (3PL), two-parameter logistic (2PL), and one-parameter logistic (1PL) dichotomous models are presented, along with the Graded Response (GR) and Generalized Partial Credit (GPC) polytomous models.
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