Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Statistics and Econometrics

In social science research, one of the main objectives of tests and surveys is to gain information about characteristics of an individual that is not directly observable. In relation to the height and weight directly seen, items like intelligence, sadness and a decent quality of life (necessarily) cannot be seen by anyone. In reality and in science, all of these variables are important to psychology. The item response theory (IRT) is one popular model for this type of work.In a world of countless tests measuring achievement, aptitude, and personality, such tests in education are used to determine if students meet educational standards.While the construction and evaluation of these tests are subject to various shortcomings, psychometricians use item response theory (IRT) as the standard set of statistical tools to analyze them.There are mathematical functions that explain the relationship between the "observable" and the "unobservable" Therefore, item response models are statistical models based on basic hypotheses about the test results.An item response model defines a correlation between the observable test performance of the evaluated individual and the unobserved traits or abilities that underlie the test performance.Different estimation methods have been developed for the item response theory (IRT) models. One of these methods is the Likelihood family which can be divided into Maximum Likelihood Estimation (MLE), Joint Maximum Likelihood Estimation (JML) and Marginal Maximum Likelihood Estimation (MML)

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