Item response theory models in the measurement theory with the use of LTM package in R

Item Response Theory (IRT) is an extension of the Classical Test Theory (CCT) and focuses on how specific test items function in assessing a construct. They are widely known in psychology, medicine, and marketing, as well as in social sciences. An item response model specifies a relationship between the observable examinee test performance and the unobservable traits or abilities assumed to underlie performance on the test. Within the broad framework of item response theory, 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 several types of IRT models such as: the Rasch, and the Birnbaum model. We present the main assumptions for IRT analysis, estimation method, properties, and model selection methods. In this paper we present the application of IRT analysis for binary data with the use of the ltm package in R.