Item response theory (IRT) models employ continuous latent variables to model dichotomous or polytomous observables, as occur frequently in assessment and social and life science settings (e.g., item responses given by students on an achievement test and scored as correct or incorrect, personal preferences rated on a Likert scale by subjects on a survey, votes in favor or against a bill by politicians, or presence or absence of a patient’s symptoms). IRT models specify the probability for an observable taking on a particular value as a function of the latent variable for the examinee (subject, politician, and patient) and the measurement model parameters for that observable. The latter are often referred to as item ...
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