8.9 Item-level Relative Fit measures (Cont’d)

If this item is a ACDM item, we have \[ P(11)-P(00)=[P(10)-P(00)]+[P(01)-P(00)] \] or \[ P(11)+P(00)-P(10)-P(01)=0 \] This is equivalent to say \[ \begin{bmatrix} 1 & -1 & -1 & 1\\ \end{bmatrix} \begin{bmatrix} P(00)\\ P(10)\\ P(01)\\ P(11)\\ \end{bmatrix}=0 \] Or, \[ \mathbf{R}\mathbf{P}=\mathbf{0} \]