, or ,

where is the parameter describing the ability of the person being tested, is the probability of getting a correct response, and is the parameter describing the difficulty of item .

The Two-Parameter Logistic Model (2PLM) is

,

where is the slope parameter; when , this is the same as 1PLM.

The Three-Parameter Logistic Model (3PLM, or Birnbaum's Model):

.

The parameter is used when item is constructed so that guessing the correct answer is possible.

The Demonstration plots the 1PLM, 2PLM, and 3PLM item characteristic curves in red, blue, and green, respectively.