In the context of an examination, the probability that an individual will respond correctly to a question (or ‘item’) is assumed to be a function of the individual’s ability.

A typical model has the formwhere θ is the parameter that represents the individual’s ability and a, b, and c are item parameters. The parameter a, with a range from 0 to 1, represents the probability of a guess being correct, the parameter b reflects the difficulty of the question, and the parameter c measures the extent to which the question discriminates between individuals with low and high ability. A related simpler model is the Rasch model.