Item Response Theory
Item response theory (IRT) was developed in response to observations that error terms in psychological measurement are frequently correlated with true scores. The measurement and analysis models of classical test theory assume that error terms are uncorrelated with true scores, that is, that the precision of measurement is equivalent across all levels of the construct being measured. The mathematical model is known as Rasch modeling, and typically the three-parameter Rasch model is invoked. The three parameters are the guessing parameter, the likelihood that an individual will get an item correct simply by guessing; the discrimination parameter or the probability of a correct response at a given level of difficulty; and the difficulty parameter or the level of skill in the construct where an item has 0.5 discrimination.
IRT allows an estimate of the precision of measurement for different levels of skill. IRT has facilitated the...