Item response theory models in the measurement theory

Item Response Theory is extension of Classical Test Theory where an item model specifies a relationship between the observable examinee test performance and the unobservable traits or abilities assumed to underlie performance on the test. Many models can be operationalized because of the large number of choices available for the mathematical form of the item characteristic curves. In this paper we introduce IRT models, we present main assumptions for IRT analysis, estimation method, properties, and model selection methods based on empirical example with the original use of application in ltm package in R.