Model type

Mathematical Forms

Item Parameter

One-parameter logistic

$P_i\left(\theta \right)=1/\left(1+{\text{e}}^{–D\ast \left(\theta -b_i\right)}\right)$

Difficulty (b)

Two-parameter logistic

$P_i\left(\theta \right)=1/\left(1+{\text{e}}^{–D\ast a_i\ast \left(\theta -b_i\right)}\right)$

Difficulty (b), discrimination (a),

Three-parameter logistic

$P_i\left(\theta \right)=c_i+\left(1-c_i\right)/\left(1+{\text{e}}^{–D\ast a_i\ast \left(\theta -b_i\right)}\right)$

Difficulty (b), discrimination (a), guessing (c)