GATE (Graduate Aptitude Test in Engineering) Psychology Research Methods and Statistics-Factor Analysis Study Material (Page 5 of 5)

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# Item Response Theory: Assumptions of IRT

Item response theory (IRT) is also known as latent trait theory, strong true score theory and modern mental test theory. It is a paradigm for the design, analysis, and scoring of tests, questionnaires, and similar instruments measuring abilities, attitudes, or other variables and is an integral part of psychometrics. It is based on the application of related mathematical models to testing data. Because it is generally regarded as superior to classical test theory, it is the preferred method for the development of high-stakes tests such as the GRE, SAT and GMAT.

This theory focuses on the item, as opposed to the test-level focus of classical test theory. The term item is use

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# Item Response Theory: Item Response Function

## Item Response Function

In three-parameter logistic (3PL) model, the probability of a correct response to an item *i* is:

Where,

is the person parameter

are the item parameters

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# Item Response Theory: Applications of IRT

## Applications of IRT

**Item Bias Analysis**: IRT provides a test of item equivalence across groups. For example, it can be tested whether an item is behaving differently for males and females. The same logic can be applied to translations of attitude scales in

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