2-parameter Normal Ogive Item Response Model
Item Factor Loading (\(\lambda)\)
Item Threshold (\(\tau)\)
$$X_{ij}^{*}=\lambda_jF_i+\epsilon_{ij}$$
$$P(X_{ij}^* > \tau|F,\lambda)=P(X_{ij}=1|\theta,a,b)=\int_{-z}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-t^2}{2}}dt$$
$$z=a*(\theta-b)$$