The 2PL Model
While the 1PL model has the advantage of simplicity, it lacks the flexibility to allow different items to have IRFs of different steepness (or slope). The 2PL model overcomes this limitation of the 1PL model by including a second parameter (ai) that controls the steepness of the IRF. As ai increases, so too does the steepness of the IRF. Because the steepness of the IRF reflects the how well the item is ability to differentiate, or discriminate, between individuals having different values of θ, ai is commonly referred to as the discrimination parameter. The 2PL model specifies the probability of correct response on the ith item (Yi = correct) using the equation