Assumptions of Item Response Theory

Any mathematical model includes a set of assumptions about the data to which the model applies, and specifies the relationships among observable and unobservable constructs described in the model. Consider as an example the well-known classical test model. With the classical test model, two unobservable constructs are introduced: true score and error score. The true score for an examinee can be defined as his or her expected test score over repeated administrations of the test (or parallel forms). An error score can be defined as the difference between true score and observed score. The classical test model also postulates that (1) error scores are random with a mean of zero and uncorrelated with error scores on a parallel test and with true scores, and (2) true scores, observed scores, and error scores are linearly related.